DFT Study of Dimerization Sites in Imidazo[1,2-a]pyridinyl-chalcone Series

Quantum chemistry methods were performed in order to characterize the chemical reactivity on series of imidazo[1,2-a]pyridinyl-chalcone (IPC). In particular, the B3LYP/6-311G(d) theory level has been used to determine parameters which characterize the global and local reactivity on five molecules of the series. These compounds differ from one to another with the aryl groups. There are: 1-(2-methylimidazo[1,2-a]pyridin-3-yl)-3-phenylprop-2-en-1-one, 3-(4-fluorophenyl)-1-(2-methylimidazo[1,2-a]pyridin-3-yl)prop-2-en-1-one, 3-[4-(dimethylamino)phenyl]-1-(2-methylimidazo[1,2-a]pyridin-3-yl)prop-2-en-1-one, 3-(2,4-dichlorophenyl)-1-(2-methylimidazo[1,2-a] py-ridin-3-yl)prop-2-en-1-one, 3-(2,4-dichlorophenyl)-1-(2-methylimidazo [1,2-a]pyridin-3-yl)prop-2-en-1-one. All results lead to finding out that local nucleophilicity and electrophilicity of compounds are not substituent-dependant contrarily to their global nucleophilicity which prove to be more sensitive to the electron-donating character of the substituents. 3-[4-(Dimethylamino) phenyl]-1-(2-methylimidazo[1,2-a]pyridin-3-yl)prop-2-en-1-one was identified as the unique nucleophile compound by global reactivity. Respectively, the carbon atoms C 5 and C 14 are the prediction sites of electrophilic and nucleophilic attacks in the molecular skeleton of both molecules. Identification of interactions centres on IPC series is of great importance for organic synthesis and medicinal chemistry where the molecular hybridization strategy is very often used to improve biological activities of interesting therapeutic systems.


Introduction
Chalcones bring together a plethora of natural and synthetic compounds, within How to cite this paper: Konate, B., Affi, S.T. and Ziao, N. (2021) DFT Study of Dimerization Sites in Imidazo[1,2-a]pyridinyl-chalcone Computational Chemistry which a keto-ethylenic system links two aromatic nuclei (aryl and/or heteroaryl rings) [1] from the carbon atom in β-position and that of the carbonyl function.

This family of compounds arouses great interest in various fields of applications.
Their true importance is based on the wide spectrum of biological activities [2] [3] [4] and on the many synthetic perspectives offered by their skeleton. The biological activities displayed by these compounds are mainly linked to the functional group enone [5] as well as to the electronic nature of the nuclei A and B due to the substituents [6] [7] [8] [9]. Imidazopyridinyl-chalcones (IPC) [10] are synthetic chalcones obtained with imidazo[1,2-a]pyridine as ring A and an aryl as ring B. Imidazopyridine nucleus is the building block in the design of several drugs [11]. In the majority of cases, chalcones have biological activities similar to those of imidazopyridine and derivatives. Undoubtedly, the chalcones carrying imidazopyridine nucleus prove to be potential sources of more biologically active molecules due to the possible conjugation effects of the two entities involved. Imidazopiridinyl-chalcones showed high nematicidal activities against drug-resistant strains of nematodes [10]. Their remarkable therapeutic properties against cancer [12] and certain bacteria [13] are also reported. These biological potentials coupled with the possible molecular diversity define a pharmacological dynamic profile which, increasingly, motivates studies of physicochemical characterizations [14] [15] and structure-activity relationships [16] in IPC series. Also, like most chalcones, the compounds IPC are susceptible to addition reactions [17]. Molecular dimerization based on the IPC entities is therefore a path that deserves serious attention for the development of novel therapeutic agents which could be probably stronger and less toxic. However, any reaction to be carried out requires precise knowledge of the chemoselectivity, the stereoselectivity and the regioselectivity. In this area, the tools of quantum chemistry and quantum theories of chemical reactivity are of great help in predicting and justifying the different selectivity. Among the theories developed and validated, nucleophilicity and electrophilicity concepts have proven to be solid in the study of molecular reactivity [18] [19] [20] [21] [22]. The different parameters defined by these concepts are global and local. In this work, we are interested in five molecules from the IPC series; four of which are substituted from the IPC nucleus by varying the aryl substituents. In Table 1, these compounds are summarized with their respective nematicidal potential pLC 100 .
The nematicidal potential pLC 100 was evaluated following the expression: where M (in g/mol) is the molecular molar mass and LC 100 (in µg/mol), the lowest concentration of tested compound that completely blocked the development of 100% of Haemonchus contortus larvae [12].
Depending on the chemistry family of substituent directly linked to carbon in the aryl, the substituted compounds could be divided into two groups: amino group (Chalc3) and halogen group (Chalc2, Chalc4, Chalc5). Moreover, the

Calculation Methods
Several theories have been developed for the study of chemical reactivity. In this work, we have used the indices and descriptors that characterize the reactivity of IPC molecules either isolated (global reactivity: static indices) either in interaction with others molecules (local reactivity: dynamic indices). The concepts of global and local reactivity make it possible to elucidate the main questions of relative reactivity, between molecules or between atoms, of the same molecule. All the reactivity parameters used come from the conceptual DFT [23].

Static Indices of Overall Reactivity
The calculations related to the global hardness (η) and global electrophilicity index (ω) in the Koopmans approximation using the energies of the frontier molecular orbital HOMO and LUMO [24] [25] according to the expressions below: These global reactivity descriptors make it possible to rationalize the possible movements of transfer and/ or acquisition of electrons by the isolated molecules. The nucleophilicity of the molecules was defined by calculating the relative nucleophilicity index N [26] [27]. The nucleophilicity scale used is that proposed by Domingo et al. [28], referenced in relation to the tetracyanoethylene (TCE) molecule and defined by the relation: By taking into account their different classification scales, the use of global electrophilicity and nucleophilicity indices makes it possible to solve the problem of compounds which can be both good nucleophiles and good electrophiles.

Dynamic Indices of Reactivity
The determination of the reactivity sites of the different IPC molecules was based on the Fukui indices calculated according to the method of the approximation of finite differences:  [29]. The sign of k f ∆ defines the reactivity character of the site. A site of the molecule whose electrophilic power is predominant will give a positive value; in the case of a predominant nucleophilic power, k f ∆ will be negative. On the other hand, the local reactivity difference index R k proposed by Chattaraj et al. [30] is also used. The values of this index make it possible to characterize the nature of the electrophilic or nucleophilic or ambiphilic power of a site within an organic molecule. The sign + or − or ± which precedes the R k values indicates, respectively, an electrophilic or nucleophilic or ambiphilic character of the considered site k. The character is all the stronger the higher the absolute value of R k . All these physicochemical parameters constitute, on the whole, solid bases for predicting chemical reactivity in IPC series, both qualitatively and quantitatively. Their determinations can only be made in the fundamental state of each of the molecular species studied, respectively. In this context, all geometry optimization calculations are followed by

Results and Discussion
The frequencies calculation which followed the geometric optimization of each molecule IPC made it possible to note the absence of imaginary frequency in all the corresponding Hessian matrices. This confirmed that each geometry of structure obtained, at B3LYP/6-311G (d) level, characterizes the fundamental state of the molecule IPC. All the chemical reactivity parameters, for each molecule, have been determined in this state. dimethylamine is predominant over its electron-withdrawing nature. This observation is in accordance with the rule in organic chemistry which retains the primacy of the mesomer effect over the inductive effect in the event of a double electronic effect of a substituent. However, in the compounds Chalc2, Chalc4 and Chalc5, this rule is taken in default: the inductive effects of halogens appear to be predominant over their mesomer effects. Taking into account these observations, the substituted molecules can be divided into two groups according to the nature of the electronic effects exerted by the substituents. There is the set of compounds Chalc2, Chalc4 and Chalc5 whose substituents affected compound Chalc1 by an electron-withdrawing effect and the second group consisting of compound Chalc3 which is marked by an electron-donor effect. Moreover, HOMO or LUMO energies constitute precious indicators for comparing electron-donor or electro-acceptor powers, in a series of molecules. Chalc3 displays the higher HOMO energy value (−5.334 eV); it is the best electron-donor.

Study of Global Reactivity
Chalc4, which has the lowest LUMO energy (−2.525 eV), is the best electron-acceptor in the series. In the case of Chalc4, there are two chlorine atoms attached to the aryl group. This suggests that the higher the number of halogens on nucleus B, the stronger the overall electro-acceptor character. In addition, the electronic configurations of the atoms which constitute IPC molecules indicate that they are Lewis bases. They are therefore structurally electron-donor. The influence of the aryl substituent on this naturally electron-donor character was highlighted from the deviations of the HOMO energies. Figure 1 shows the diagram established according to the values of the HOMO energy variations in relation to the unsubstituted compound Chalc1.
The diagram illustrates well the electronic effect of each substituent in the aryl group. On the electron-donating scale, ternary amines are far more electron-donor by resonance than halogens, which are very much less electron-donors. The electron-donating power of the studied molecules is then strong when the aryl  substituent is a good electron-donor but very weak when the substituent is a strong electron-withdrawing agent. For example, in the case of halo-aryl compounds (Chalc2, Chalc4, Chalc5), the negative values HOMO E ∆ clearly reflect the strong attenuation of the electron-donating character due to the presence of halogens and the tendency of the molecules rather towards the global electro-accepting character. Under these conditions, the compounds Chalc2, Chalc4 and Chalc5 become more susceptible to attack a nucleophile. The compound Chalc3 could play the role of electron-donor in IPC intermolecular interactions.
Therefore, if we calculate the differences in energies according to the relationship: the sequence of evolution in increasing order of the strength of intermolecular interactions coded 3 IPC i → , between Chalc3 and another IPC (Chalci), is presented as follows: The strongest predicted interaction 3 4 IPC → , is associated with an energy difference of 2.809 eV with the substituted molecule Chalc4 and that of lesser force, 3 1 IPC → , with an energy difference of 3.069 eV implies the unsubstituted molecule Chalc1. In fact, polar interaction is all the stronger when the energy difference between nucleophile and electrophile is small. In the case of molecules in the IPC series, any substitution carried out at the level of the aryl group is always favourable to the strengthening of the nucleophilic-electrophilic interactions. The nucleophilic and electrophilic characters of the substituted compounds are then rationalized using the global nucleophilicity and electrophilicity indices.
The values of electronegativity χ, of hardness η and of the global electrophilicity ω and nucleophilicity indices N are reported in Table 3.
According to the values in Table 3, two evolution trends can be defined by following the substituted compounds with reference to the unsubstituted com-   spectively, as follows: Analysis of these evolution sequences shows that they are related to the LUMO and HOMO energies evolution orders, respectively. In fact, the electro- Computational Chemistry reactivity criteria remain very important for the study of the reactivity and selectivity trends of specific sites within a molecule. The local reactivity approach therefore makes it possible to clearly identify the privileged atoms by which a molecule will establish the bonds during molecular interactions. In the case of this study, the isodensity maps relating to the frontier orbitals (HOMO, LUMO) of the different molecules clearly indicate that the HOMO is located mainly on the imidazopyridine nucleus when the LUMO is largely around of the keto-ethylenic system. This therefore supposes that the probable transfer of the electron density takes place from the atoms of the imidazopyridine nucleus to the atoms which constitute the keto-ethylenic system.

Study of Local Reactivity
In this study, the interest was focused on the heavy atoms of the basic skeleton of imidazo[1,2-a]pyridinyl-chalcone derivatives. Figure 2 shows the numbering of the atoms in the molecules considered.
The analysis of the isodensity maps of HOMO and LUMO, respectively, allowed identifying the potential interaction sites in the compounds studied. From one molecule to another, the atoms which contribute highly to frontier orbital formation stay the same. In fact, the largest lobes characterize the highest electron density in the case of HOMO and the lowest electron density in the case of LUMO, around the atom implicated. On the maps of HOMOs, the four largest lobes contain the carbon atoms C 2 , C 6 , C 7 , C 9 , C 5 and the nitrogen N 3 . All of these atoms are the likely nucleophile sites in IPCs. On the maps of LUMOs, the carbon atoms C 11 , C 13 and C 14 which belong to the two largest lobes are the likely electrophile sites. Figure 3, related to the compound Chalc1, allows illustrating these observations.  Regarding the site C 11 , it belongs to the carbonyl bond, the presence of which is very useful for the manifestation or even the preservation of the biological properties of chalcones. Thus, the different atoms whose reactivity has been demonstrated are the atoms C 2 , C 7 , C 8 , C 9 , C 5 , C 13 , C 14 and N 3 of the imidazo[1,2-a]pyridinyl-chalcone nucleus.
The local reactivity indices of all of the interaction sites are determined according to Fukui theory. Their tendency to behave like an electrophile or a nucleophile will be estimated by following the nature of electrons movement caused by the aryl substituents. In Table 4, the different values of the dual index is one of the very precious and useful parameters for rationalizing the sensitivity of a site within a given molecule to an electrophilic or nucleophilic attack, especially when this site displays a double tendency of reactivity. Also, based on the indices analysis, k f ∆ and R k , the sign provides information on the charge inequalities between nucleus and electronic cloud and, consequently, on the predominant reactivity of site k within the molecule. According to Table 4, and considering all five molecules of the series, the higher k f ∆ values are observed for the carbon atom C 14 followed closely by the nitrogen atom N 3 when the lower values are found with the atoms of carbon C 2 and C 5 , within each molecule. Concerning the atom C 14 , the k f ∆ values are all positive, thus showing that this atom has a great susceptibility to increase its electronic density in the event of electrons gained by the molecule. C 14 is then an electron deficient site and its reactivity is therefore very strong towards a nucleophile. Moreover, the Fukui function k f + which makes it possible to highlight the electrophilic reactivity of a site relatively to a nucleophilic attack displays its highest values with the atom C 14 whatever the molecule. Regarding the atom C 5 , the k f ∆ negative values reflect its susceptibility to have a high electron density even if the molecule loses electrons; it is then rich in electrons and therefore the most reactive centre towards an electrophile. Also, the higher values of the Fukui function k f − recorded at this site, whatever the substitution, corroborate this observation. Consequently, the carbon atoms C 14 and C 5 constitute, in the order, the most reactive electrophilic and nucleophilic centres, in the IPC series. All the sites k with positive values of k f ∆ and R k indicate the potentially electrophilic centres, while the negative values characterize the potentially nucleophilic centres, within the molecules. Thus, analysing k f ∆ and R k values, in the decreasing order of electrophilic reactivity, the site C 2 directly follows the site C 14 when the site N 3 occupies the second place of nucleophilic reactivity after the site C 5 , in the decreasing order, on all the molecules. Indeed, and particularly within the compound Chalc3, although 13 7 0.091 0. 048 indicates a higher nucleophilic reactivity of C 13 relatively to C 7 , the value 0.249 eV k R = ± for atom C 13 rather reflects a no less stable nucleophilic behaviour. In fact, the value 0.249 eV k R = ± is characteristic of an ambiphilic site, i.e. which behaves as both nucleophile and electrophile. This result agrees with the local chemical reactivity in α, β-unsaturated keto-ethylenic systems where the localization of π electrons due to conjugation keep the α-position carbon C 13 in the same ethylenic environment; this carbon atom doesn't lose or gain electrons during the movement of electrons. Another notable remark concerns the R k values for site C 8 . Another remarkable observation is the ± sign which pre-DOI: 10.4236/cc.2021.91001 12 Computational Chemistry cedes all the R k values for C 8 site, on all of the studied molecules. The presence of this sign reveals that the carbon C 8 is an ambiphilic site within the compounds IPC. In addition, the inductive and resonant effects exerted by the substituents attached to the aryl nuclei can possibly influence the sensitivity to attack of the predicted privileged sites C 5 and C 14 . The sense of influence on the reactivity of the sites is then highlighted for the best prediction of intermolecular interactions in the IPCs series. The comparative study was carried out based on the local reactivity difference index R k . The higher the absolute value of the index R k of site k, the greater the activation of the site nucleophilicity. At the C 5 site, the evolution sequence observed in ascending order of the absolute values of this index is presented below: Absolute indices of the halo-aryl compounds IPC are all higher than that of the amino-aryl compound IPC. Thereby, the nucleophilic reactivity of the site C 5 within the molecules IPC is higher in the presence of halogens. This sequence of evolution is opposite to that of global nucleophilicity for these same compounds.
The nucleophilic character of the site C 5 is more and more strengthened when the compound IPC becomes less and less nucleophilic. The high nucleophilicity of the site C 5 within a molecule is therefore not directly linked to the high nucleophilicity of the molecule. The best electron-donor compound in the series, Chalc3, has the weak electron-donor nucleophilic site C 5 while the best electro-acceptor compound in the series, Chalc4, has the best electron-donor nucleophilic site C 5 . Consequently, substitution with a group having a strong electron-donating character proves unfavourable to the nucleophilic reactivity of site C 5 . For example, in the case of Chalc3, the substituent group of dimethylamine (strongly electron-donor) caused the nucleophilicity of the site to regress by around 43.48% compared to 1.80% in Chalc2 with fluorine (weakly electron-donor).
As regards the electrophilic site C 14 , considering the index R k values, the increasing order of electrophilic reactivity within the different molecules is: This sequence of evolution for the electrophilic reactivity of the site C 14 within the compounds IPC is not in agreement with the evolution of the global electrophilic behaviour of the studied molecules. However, it seems to correspond to the nucleophilic behaviour evolution of these compounds. The highest electrophilic reactivity of the site C 14 is recorded with the best nucleophilic compound Chalc3 in the series when the weakest is found with Chalc5, a less nucleophilic compound. Consequently, substitution on the aryl nucleus with a strongly electron-donating fragment is favourable to strengthening the ability of the electrophilic site C 14 to bind to a nucleophilic site. For example, the improving effect of the electrophilic reactivity of C 14 is around 39.49% with dimethylamine compared to 9.58% with fluorine, by substitution. Chalc2, Chalc4 and Chalc5 belong to the halo-aryl group. Thereby, the above sequence indicates that halogens better promote the nucleophilic character of nitrogen in the IPCs series by the substitution. Nevertheless, the sequence (xvii) of evolution for the nucleophilic character of the site N 3 is in the opposite direction to that of the electrophilic character of the site C 14 (xiii) defined following the index R k values. This fact means that any substitution which reinforces the nucleophilic character of nitrogen N 3 disadvantages the electrophilic character of the carbon C 14 . Such a phenomenon is therefore beneficial to the improvement of the nematicidal activity in the IPC series.
All of these observations are very interesting. They could help in the implementation of strategies for improving nematicidal properties in the IPC series.

Conclusion
The chemical reactivity of the compounds in imidazo[1,2-a]pyridinyl-chalcone series is predictable by quantum chemistry methods using conceptual DFT reactivity descriptors. In this series, the effects of substitution on the determined pa- The carbon C 14 , in β-position in the keto-ethylenic system was designated as the more potential electrophilic centre. From one molecule IPC to another, the electrophilic or nucleophilic natures as well as the order position of these two preferential sites were independent of the substituents nature and electronic effects.
Therefore, in attractive intermolecular interactions in the IPC series, the most likely bond will be established between carbon atoms C 14 and C 5 , regardless of the molecules. This observation was of capital importance in the sense that the formation of dimers based on the IPCs obeyed the same mode of connection whatever the substitution on the aryl group. Finally, the structure-activity analysis revealed that the inactivation of the electrophilic character of the site C 14 by substitution on the B nucleus or by formation of a bond with this site would be favourable for improving the IPC series. The results of this study provide an interesting basis for the study of dimerization in the IPC series.