1 Introduction

The pyridazinone ring has been studied in the past and it has been discovered to possess a variety of biological activities. Because these compounds include pyridazinone moieties, they have different pharmacologic actions. The use of pyridazinones as anti-inflammatory drugs [1], analgesics [2, 3], COX inhibitors [4], aldose reductase inhibitors [5], and anticancer drugs [6, 7] has increased significantly in recent years. Also, several medications like the painkiller emorphazone and the medicine zardaverine contain the pyridazinone ring (phosphodiesterase inhibitor). The anti-inflammatory, selective COX-2 inhibitor, antibacterial, and anti-proliferative properties of its derivatives have been well documented [8, 9].

To improve the bioligical activity of pyridazinone [10,11,12,13], chemical reactions have been performed on this starting material of 2 H-pyridazi-3-one, in the synthesis of novel pharmacological molecules, 2 H-pyridazi-3-one molecule is frequently used as a starting material in 3 + 2 cycloaddition reactions to form nitrogen rings [14,15,16]. The ability of 6-methyl-4,5-dihydro 2 H-pyridazi-3-one to participate in cycloaddition reactions can be attributed to the presence of its pyridazine functional group, which has a high reactivity towards dipoles (Scheme 1) [16].

scheme 1

Scheme 1

[3 + 2] cycloaddition reactions involve the formation of cyclic compounds by combining three atoms (3-component) with two atoms (2-component), this type of reaction is also known as 32CA cycloaddition. The most common example of a 32CA cycloaddition reaction is the Huisgen reaction, known as azide-alkyne cycloaddition (Scheme 2). In this reaction, an azide (3-component) reacts with an alkyne (2-component), which is a molecule containing a carbon-carbon triple bond. The reaction leads to the formation of a cyclic compound called a tetrazole. This type of reaction is widely used in synthetic chemistry for the construction of complex molecular structures and these cycloaddition reactions offer an efficient synthetic route for the formation of carbon and heterocyclic rings, making them an important class of reactions in organic chemistry [17].

scheme 2

Scheme 2

The synthesis of novel compounds with high nitrogen content may be made possible by the dipolarity of nitrilimines and their propensity to engage in a variety of reactions. Nitrilimines have known precursors, including hydrazonyl halides and 2,5-disubstituted tetrazoles. These dipolar nitrilimine compounds have intrinsic value since they can perform 1,3-dipolar cycloaddition processes (Scheme 1), the reactivity of nitrilimines have been extensively studied both theoretically and experimentally [18,19,20,21].

Quantum methods offer powerful tools for understanding molecular structure, spectroscopic properties and chemical reactions [22, 23]. The DFT (density functional theory) method is capable of predicting spectroscopic properties such as UV-vis and nuclear magnetic resonance (NMR) spectra [22, 23]. It can also be used to study chemical reactions and to predict reaction mechanisms [24,25,26,27,28,29,30,31,32]. Within the framework of the DFT method, with a fairly recent study proving that MEDT delivers more information than FMO [33], the molecular electron density theory (MEDT) has recently emerged as an alternative to the frontier molecular orbital theory (FMO) for the study of chemical structure and reactions.

Recent work on the theoretical understanding of 32CA reactions based on molecular electron density theory (MEDT) has established a very good correspondence between the electronic structure of three-atom compounds (TACs) and their reactivity. Therefore, based on the electronic structure of the simplest TACs, 32CA reactions have been classified into pdr-type, pmr-type, zw-type and cb-type reactions such that, while pdr-type 32CA reactions can be easily approved, zw-type 32CA reactions require adequate nucleophilic/electrophilic activations to occur (Fig. 1).

Fig. 1
figure 1

The proposed reactivity types in 32CA reactions and the electronic structure of TACs.

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In this study, MEDT has been used to elucidate the mechanism and different selectivities of the [3 + 2] cycloaddition reaction between 6-methyl-4,5-dihydro-2 H-pyridazi-3-one and nitrilimine, which was experimentally studied by Rakib et al. [16] (Scheme1), and also the molecular docking has beenused to predict the affinity of the products studied against corona virus (Fig. 2).

Fig. 2
figure 2

Pyridazine derivatives (P1-P6) docked into the main protease COVID-19 (6LU7, 6Y84 and 6YB7) compared to ribavirin

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2 Computational Method

All the computations are processed in Gaussian 09 [34]. To characterize and locate stationary points where the transition phases have just one imaginary frequency, frequency computations were used, while all frequencies are positive for the reactants and products [35]. The IRC has been utilized to survey the reaction path from its initial state to its final state; it also allows to determinate the intermediate steps and the associated activation barriers [36]. The PCM (Polarizable Continuum Model) [35, 37,38,39,40] was employed to examine the effect of the solvent on the optimized structures. The electronic chemical potential occurs a thermodynamic competence that describes the facility of a reactants to gain or lose electrons from its electronic structure and is designated:\(\varvec{\mu }=\frac{{E}_{L}+{E}_{H}}{2}\). The Chemical hardness is a concept used in chemistry to describe the ability of a substance to resist disruption of its electronic structure which is defined by:\(\eta ={E}_{L}-{E}_{H}\), using the energies of the HOMO and LUMO boundary molecular orbitals, are given by EH and EL. The global electrophilicity index (w) is a quantity used in chemistry to measure the tendency of a molecule to react as an electrophile, i.e. to attract electrons from another molecule to form a chemical bond and is defined by the following formula: \({\upomega }=\frac{{\mu }^{2}}{2\eta }\), [41] contrary to the electrophile index, the index of nucleophilie (N) is a concept useful to check the tendency of a molecule to react as a nucleophile, i.e. to give electrons to another molecule to form a chemical bond, defined as: E = EHOMO (Nu)-EHOMO (TCE) [42]. Parr functions have been employed to find local indices, which are basic spin wave functions that are used in quantum chemistry to describe the electronic spin distribution in molecules [43]. The electron localization function was described employing a Topmod software, this ELF is used to provide a representation of the distribution of electrons [44, 45].

Water molecules attached to the receptors were removed, and polar hydrogen atoms were added to the receptors using Autodock Tools (ADTs) [46]. Gaussian 09 Rev. A 11.4 software program was used to obtain optimized structures of [1, 2, 4]triazolo[4,3-b]pyridazine derivatives, which created files with the extension *.pdb using these structures. The central grid box is approximately (13.073, 22.467, and 5.557 ) based on the ligand position in the protein, and the grid maps were constructed to 60 in the X, Y, and Z dimensions. Discover Studio 3.5 from Biovia and PyMol 2.3 software was used for 2D and 3D molecular interactions of the P1-P6 ligands in the active sites of the 6LU7, 6Y84, 6YB7 receptors [47, 48].

3 Results and Discussion

3.1 Analysis of Reactants

Table 1 includes information on the two reagents, 6-methyl-4,5-dihydro 2 H-pyridazi-3-one and 2-ethoxy-2-oxo-1-(p-tolyldiazen-1-ium-1-ylidene)ethan-1-ide, including their chemical potential, chemical hardness, electrophilicity index, and nucleophilicity index.

Table 1 Chemical electron potential, chemical hardness, global electrophilicity index, and global nucleophilicity index at B3LYP/6-31G(d), all measured in electron volts (eV)
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From the values obtained of the chemical potential µ of dipole (-3.67) and dipolarophile (-3.44) we notice a slight difference in favor of the dipolarophile, which will give a slight charge transfer between these two entities (no polar reaction). In accordance with the global nucleophilicity and electrophilicity values, it can be concluded that the dipole will behave as an electrophile and the dipolarophile will act as a nucleophile [49], this will be confirmed by the charge transfer at the transition structures.

The reactivity of organic compounds in chemical processes is predicted using Parr functions [43], they can also be used to compare the local reactivity of various compounds and compared to each other. However, it should be noted that Parr functions do not provide any qualitative suggestion of the reactivity of molecules if the reaction is non-polar and when we have similar reagents, in this case, several studies used the electrophilic Parr functions, the first bond will be formed on the center that has the largest value [50,51,52], we have presented the electrophilic Parr functions \({ P}_{k}^{+ }\) of 1 in Fig. 3.

Fig. 3
figure 3

Electrophilic Parr functions of the 6-methyl-4,5-dihydro 2 H-pyridazi-3-one 1

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The results mentioned in Fig. 1 show that the C6 atom has the highest value (0.39) and therefore it is the highly electrophilic centers. Consequently the establishment of the first new bond will be on the C6 carbon; this result is consistent with the experiment [16].

3.2 Electron localization Function (ELF) Study of Reagents

The nature of the bonds in the system can be known from the synaptic order. Monosynaptic basin are connected to only one core basin, they represent free pairs. A bond between two atoms is revealed by a disynaptic basin connected to both their core basin [30, 31]. In order to comprehend the reactivity of the dipole employed in this reaction, an elf analysis of the reagents has been realized, The ELF localization domains with the highest density of valence basins are represented in Fig. 4. MEDT studies [25] on [3 + 2] cycloaddition reactions have revealed a highly correlated electronic structure of the simplest TACs with its reactivity [26], 32CA reactions have been divided into the pdr, pmr, zw, and cb type reactions based on the electronic structure of the most basic TAC (Three-atom-components) [25, 26]. (Fig. 1).

Fig. 4
figure 4

Shows the ELF localization domains with the largest density of valence basins (red color represents monosynaptic basin, green color represents disynaptic basins, purple color represents the center atom, and blue color represents the surface of the hydrogen atom)

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Because of the asymmetry of 2, the ELF topological analysis of this TAC has revealed an asymmetric electron density distribution. Thus, while two disynaptic basins V(N4,C7) and V‘(N4,C7) are observable in the two C-N bonds regions with an electron population of 4.66e, a disynaptic basin V(N3,N4) with a population of 2.26e and a monosynaptic basin V(C7) of a value of 1.55e is found at the two C7 carbons. There is also a monosynaptic basin V(N4) carried by the N4 nitrogen atom with a population of 3.17e. As a consequence, the ELF topology of 2 suggests that this TAC has a pseudodiradic electronic structure that enables it to participate in [3 + 2] cycloaddition reactions as pdr-type reactions.

Five monosynaptic basins have been identified by topological analysis ELF of reagent 1: two are carried by oxygen atoms, with a total integrated value of V(O1) = 5.39e, and two more are carried by nitrogen atoms, with a total integrated value of V(N2) = 2.1e. We observed the presence of a bisynaptic basin between carbon C3 and oxygen O1, with a population of V(C3,O) = 2.33e, and one monosynaptic basin carried by the nitrogen atom N1, with a total integrated with a population of V(N2) = 2.84e and a second, similarly significant disynaptic basin between the elements carbon (C6) and nitrogen (N1), with the value V(C6,N1) = 3.14e indicating that the link between these two elements is highly electron-enriching and has been reactivated. This proves that this cycloaddition reaction is chemiosectivity in clear agreement with experimental [16].

3.3 The ThermoChemistry Study

The three thermochemistry parameters for investigation are enthalpy (H), entropy (S), and Gibbs free energy (G). Since the reactants being analysis are asymmetrical, there are six different reaction pathways are studied (Scheme 3). Figure 5 displays the energy profile, and Table S1 provides the thermochemical values (supplementary file).

Scheme 3
scheme 3

Reaction paths of the cycloaddition between 6-methyl-4,5-dihydro 2 H-pyridazi-3-one 1 with 2-ethoxy-2-oxo-1- (p-tolyldiazen-1-ium-1-ylidene)ethan-1-ide 2

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Fig. 5
figure 5

The energy profile of the cycloaddition between 6-methyl-4,5-dihydro 2 H-pyridazi-3-one 1 and 2-ethoxy-2-oxo-1-(p-tolyldiazen-1-ium-1-ylidene)ethan-1-ide 2

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From Fig. 5, some intriguing conclusions can be made: (i) The free energies of reaction found for products 4, 6, 7 and 8 are negative, so all five reactions are thermodynamically possible. (ii) The free energy of reaction of product 3 and 5 are positive, so the formation of these products is thermodynamically impossible. (iii) The formation of products 3 and 5 is endothermic, with ∆G(3) = 29.78 and ∆G(5) = 35.09 (kcal/mol), whereas the remaining four reaction pathways are exothermic, with free reaction energy values of: ∆Gr(4) = − 2.34, ∆Gr(6) = − 8.98, ∆Gr(7) = −16.12 and ∆Gr(8) = − 3.70 (kcal/mol). (iv) the free energy of activation of six reactions paths are: TS1 = 45.24 (kcal/mol), TS2 = 19.99 (kcal/mol), TS3 = 35.09 (kcal/mol), TS4 = 19.83 (kcal/mol), TS5 = 25.16 (kcal/mol) and TS6 = 27.48 (kcal/mol).

The thermodynamic profile confirms that the formation of product 6 is kinetically and thermodynamically favorable; this result confirms that this reaction is regio-, stereo and chemospecific [16].

We have collected in Table 2 the formation rates of the studied products 3, 4, 5, 7 and 8 compared to the most favorable product 6, these rates are calculated by the following relation.

$${\varvec{K}}_{\varvec{P}}=\frac{{\varvec{T}\varvec{K}}_{\varvec{B}}}{\varvec{h}{\varvec{C}}_{0}}{\varvec{e}}^{\frac{{-\varDelta \varvec{G}}^{\#}}{\varvec{R}\varvec{T}}}$$

With\({K}_{B}\), h, \({C}_{0}\) and R noted respectively Boltzmann’s constant, Plank’s constant, standard concentration (1 mol.L-1) and since we worked with a room temperature T = 298 K the gas constant R = 1.987 cal.K− 1.mol− 1.

The formula below is used to compute the percentage of products:

$$\frac{{\mathbf{K}}_{\mathbf{T}\mathbf{S}\mathbf{T}}\left(7\right)}{{\mathbf{K}}_{\mathbf{T}\mathbf{S}\mathbf{T}}\left(\mathbf{P}\right)}=\frac{\frac{{\varvec{T}\varvec{K}}_{\varvec{B}}}{\varvec{h}{\varvec{C}}_{0}}{\varvec{e}}^{\frac{{-\varDelta \varvec{G}}^{\#}\left(7\right)}{\varvec{R}\varvec{T}}}}{\frac{{\varvec{T}\varvec{K}}_{\varvec{B}}}{\varvec{h}{\varvec{C}}_{0}}{\varvec{e}}^{\frac{{-\varDelta \varvec{G}}^{\#}\left(\varvec{P}\right)}{\varvec{R}\varvec{T}}}}={\frac{{\mathbf{K}}_{\mathbf{T}\mathbf{S}\mathbf{T}}\left(\mathbf{P}\right)}{{\mathbf{K}}_{\mathbf{T}\mathbf{S}\mathbf{T}}\left(7\right)}=\varvec{e}}^{\frac{{\varDelta \varvec{G}}^{\#}\left(\varvec{P}\right){-\varDelta \varvec{G}}^{\#}\left(7\right)}{\varvec{R}\varvec{T}}}$$
Table 2 compares the formation rates (R) of the investigated products 3,4,5, 7, and 8 to the most advantageous product 6
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From Table 2, it can be seen that the speed of the reaction pathway which forms the product 6 is high compared to the other pathways, and its can too that the rate reaction R6 slightly higher than rate reaction of the product 4, which confirms that this reaction is regio- and chemopecific; this outcome is relatively consistent with the experimental [16].

Fig. 6
figure 6

The transition state structures in the gas and in THF (the values in brackets in THF)

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The values of the charge transfer have been assessed for all optimized TS structures using a natural population analysis in terms of the residual charge on reagent 1. The positive values of the global electron density transfer (GEDT) listed in Fig. 6, indicate that the electron density flux occurs from reagent 1 acting as a nucleophile to the dipole acting as an electrophile, which is in good agreement with the values of the electron chemical potentials covered in the CDFT part. The fact that the results were higher than 0.20e indicates that the DA reactions under study had a high degree of polarity [52, 53].

3.4 Molecular Docking

The antiviral activity of six [1, 2, 4]triazolo[4,3-b]pyridazine derivatives was investigated against the crystal structures of severe acute respiratory syndrome-coronavirus (SARS-CoV-2) protease or COVID-19 main protease (Mpro) in access numbers 6LU7 [54], 6Y84 [55], 6YB7 [56, 57].

The antiviral drug ribavirin (1-β-D-ribofuranosyl-1,2,4-triazole-3-carboxamide) synthesized in 1972 has shown broad spectrum antiviral activity against both RNA and DNA viruses and recently for SARS-CoV-2 infections [55]. The interaction profiles of [1, 2, 4]triazolo[4,3-b]pyridazine derivatives are compared with ribavirin and showed in Table S2. The obtained results in Table S2 indicated that the binding energies (kcal/mol) for 6YB7 crystal structure of the SARS-CoV-2 main protease (306 sequence length and 1.25 Å resolution) follow the order of −6.41 > −6.34 > −6.25 > −6.24 > −6.14 > −6.11 > −5.61 kcal/mol for P3 > P5 > P2 > P1 > P6 > P4 > Ribavirin, respectively. The binding energies (kcal/mol) for 6LU7 crystal structure of the SARS-CoV-2 main protease follow the order of −6.65 > −6.08 > −6.05 > −5.95 > −5.72 > −5.65 > −5.60 kcal/mol for P3 > P4 > P1 > P2 > P5 > P6 > Ribavirin, respectively. The binding energies (kcal/mol) for 6Y84 crystal structure of the SARS-CoV-2 main protease follow the order of −8.69 > −7.81 > −7.53 > −6.38 > −6.26 > −5.92 > −5.49 kcal/mol for P3 > P1 > P6 > P5 > P4 > P2 > Ribavirin, respectively. The compound P3 carrying the phenyl group with the nitro group was found to have good antiviral activity in comparison with the standard antiviral drug (ribavirin) and other studied derivatives. Therefore, the results obtained for [1, 2, 4]triazolo[4,3-b]pyridazine derivatives (P1-P6) confirm that P3 may be the best antiviral drug.

Molecular modeling studies (Figure S2) illustrate the results of the bonding interactions for the docking of compound P1-P6 and ribavirin with amino acids of the 6LU7, 6Y84, 6YB7, respectively, in Fig. 7 shows the interactions of P3 with amino acids of 6LU7, 6Y84 and 6YB7. All P1-P6 compounds can form conventional hydrogen bonds between THR199 / LEU287 active sites of 6LU7 protein and the O atom of the C = O group / N atom of 1,2,4-triazolopyridazine ring at distances of 2.1–3.0 Å / 3.7–5.1 Å, respectively. The visualization of ligand interaction with the amino acid residues of Covid-19 Mpro (Fig. 7) shows that an N atom of 1,2,4-triazolopyridazine ring for P1, P4, P6 form a conventional hydrogen bond with the LYS5 (2.6 Å, 2.7 Å, 2.0 Å) amino acid of 6Y84 protein, respectively. The oxygen atom on the carboxylate chain for P1, P2, P3, P6 derivatives forms a conventional hydrogen bond with the VAL77, VAL77, ASN63, VAL77 residues of 6YB7 protein.

Fig. 7
figure 7

Two and three-dimensional visualizations of docking of [1, 2, 4]triazolo[4,3-b]pyridazine derivative docked in COVID-19 main protease (6LU7, 6YB4 and 6YB7) compared to the Ribavirin

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4 Conclusion

Theoretical study of the behavior of 6-methyl-4,5-dihydro-2 H-pyridazi-3-one (1) towards 2-ethoxy-2-oxo-1-(p-tolyldiazen-1-ium-1-ylidene)ethan-1-ide (2) allowed us to conclude that in the presence of a stoichiometric amount of (2), 6-methyl-4,5-dihydro 2 H-pyridazi-3-one (1) reacts regio- and chemioselectively through its C3 = C4 double bond. Thus, in this [3 + 2] cycloaddition reaction, CDFT demonstrates that (1) behaves as a nucleophile and (2) as an electrophile. Parr nucleophilic functions and ELF topological analysis of the reactants indicate that the C6 = N1 double bond of 6-methyl-4,5-dihydro-2 H-pyridazi-3-one (1) is more electron rich, showing that this bond is more reactive, in excellent agreement with experiment, therefore, the reaction is highly chemo- and regioselective. In addition, a docking study of P1-6 cycloadducts, docked in Covid-19 major protease (6LU7) in comparison with ribavirin was performed; the results indicate that P3 cycloadducts could serve as antiviral drug.