A Multifield Study on Dimethyl Acetylenedicarboxylate: A Reagent Able to Build a New Cycle on Diaminoimidazoles

A new effective method for the synthesis of imidazo[1,5-b]pyridazines derivatives (yields = 68–89%) by the interaction of 1,2-diamino-4-phenylimidazole with DMAD, in methanol and in the presence of a catalytic amount of acetic acid, is proposed. The course of reaction has been examined by classical organic methods, HPLC-MS analysis, and quantum-chemical calculations.


Introduction
Several natural biologically active systems (from chlorophyll to hemoglobin) and many natural and synthetic drugs (from penicyllin to sulfadiazine) contain in their structure heterocyclic systems (mono-or poly-cyclic) holding different hetero-atoms (from nitrogen to oxygen or sulphur). This is likely one of the reasons that so many chemists study the syntheses, the reactivities, andthe properties of several heterocyclic compounds.
We have focusedour attention onboth mono-and poly-cyclic systems. Now, we are turning our interest to the study of a reaction able to "build" a new ring on an already existing one.
Vice versa, in the instance of 2-amino-4-aryl-1arylideneaminoimidazoles 39b, the previously described pyrroles 40b in a mixture with benzonitriles 42 were isolated after boiling. Moreover, performing the reaction at room temperature the formation of dimethyl-1-(2-amino-1-benzylideneamino-4-aryl-1N-imidazol-5yl)fumarates 43 was observed (Scheme 6). Looking at the complex aforementioned results, we have focusedour attention onthe study of the reaction of DMAD with non-symmetric polynucleophiles deriving from 1,2-diaminoimidazoles: the influence of reaction conditions on the regioselectivity will be examined using classical organic synthesis and quantum chemical calculations.

Results and Discussion
Considering the fact that the observed course of reaction of DMAD 1 with some nucleophiles depends on the nature of the solvent, first we have investigated and selected the optimal reaction conditions, examining the possible interactions of 1 with 1,2-diamino-4-phenylimidazole 44a. Based on the literature data and considering the solubility of the starting diamine, we have chosen thepossible solvents benzene, dioxane, chloroform, methylene chloride, methanol, and ethanol. The composition of the reaction mixture was assessed using the absolute normalization method based on HPLC-MS analysis. The signals were interpreted on the basis of preliminary calculated weights, in the form of molecular ions with [M+H] + of all the possible initial, intermediate, and expected final compounds. Samples were treated for 0, 60, and 120 min. It should also be noted that under the conditions of our HPLC-MS experiment, DMAD was not protonated or detected at a given wavelength. The results obtained are portrayedin Table 1. As can be observed, when solvents such as benzene, dioxane, chloroform, or methylene chloride were used, the highest conversion of the starting diamine after 2 h of boiling is about 37-65%. In this case, the mass spectra of the reactionsindicatesignals of the formed intermediates and products of their intramolecular cyclization. A different behavior was observed when methanol or ethanol were used as solvents: complete conversion of 1,2-diamino-4-phenylimidazole occurred in 2 h. However, using Scheme 6. Interaction of DMAD with 2-amino-4-R-1-arylideneaminoimidazoles.
Looking at the complex aforementioned results, we have focusedour attention onthe study of the reaction of DMAD with non-symmetric polynucleophiles deriving from 1,2diaminoimidazoles: the influence of reaction conditions on the regioselectivity will be examined using classical organic synthesis and quantum chemical calculations.

Results and Discussion
Considering the fact that the observed course of reaction of DMAD 1 with some nucleophiles depends on the nature of the solvent, first we have investigated and selected the optimal reaction conditions, examining the possible interactions of 1 with 1,2-diamino-4-phenylimidazole 44a. Based on the literature data and considering the solubility of the starting diamine, we have chosen thepossible solvents benzene, dioxane, chloroform, methylene chloride, methanol, and ethanol. The composition of the reaction mixture was assessed using the absolute normalization method based on HPLC-MS analysis. The signals were interpreted on the basis of preliminary calculated weights, in the form of molecular ions with [M+H] + of all the possible initial, intermediate, and expected final compounds. Samples were treated for 0, 60, and 120 min. It should also be noted that under the conditions of our HPLC-MS experiment, DMAD was not protonated or detected at a given wavelength. The results obtained are portrayedin Table 1. As can be observed, when solvents such as benzene, dioxane, chloroform, or methylene chloride were used, the highest conversion of the starting diamine after 2 h of boiling is about 37-65%. In this case, the mass spectra of the reactionsindicatesignals of the formed intermediates and products of their intramolecular cyclization.
A different behavior was observed when methanol or ethanol were used as solvents: complete conversion of 1,2-diamino-4-phenylimidazole occurred in 2 h. However, using ethanol, the formation of the target reaction product was significantly low, in line with an ongoing process of transesterification of the ester group. Moreover, the formation of a We have previously observed that heterocyclization reactions involving diaminoimidazole are accelerated by acid catalysis (for example, by acetic acid) [43][44][45]. In this case, we have observedthat the addition of acetic acid, using methanol as a solvent significantly affected the reactivity. In fact, as presented in Table 1, the addition of catalytic amounts of acetic acid allows a complete conversion of the reactant in 60 min. It should be noted that, on the contrary, conducting a reaction in a mixture of acetic acid and methanol (1:1) reduces the reactivity of the reagents and leads to the formation of several by-products.
Thus, it was discoveredthat the reaction between dimethylacetylenedicarboxylate 1 and 1,2-diamino-4-phenylimidazoles 44a-e proceeds most smoothly when methanol with the addition of a catalytic amount of acetic acid was used as solvent. In this case, the complete conversion of the starting diamine and the maximum yield of the target product were achieved after an hour of boiling the reagents.
Considering the polynucleophilic nature of the starting 1,2-diaminoimidazoles 44a-e, Scheme 7 reports the structures of all possible intermediates of their interaction with DMAD 1. Thus, during the first step, the nucleophilic addition of 44a-e on the triple bond of 1 due to the nucleophilic CH, NH, and NH 2 groups, in addition to the nitrogen atom of the cycle, can lead to the formation of the intermediates A-D. The resulting Michael adducts can undergo intramolecular cyclization, due to the "near" or "far" carboxyl group, with the formation of the corresponding products 45-50.
Molecules 2022, 27, x FOR PEER REVIEW 6 of 21 ethanol, the formation of the target reaction product was significantly low, in line with an ongoing process of transesterification of the ester group. Moreover, the formation of a mixture of ethyl and methyl esters makes more complex the identification/analysis of the products of reaction.
We have previously observed that heterocyclization reactions involving diaminoimidazole are accelerated by acid catalysis (for example, by acetic acid) [43][44][45]. In this case, we have observedthat the addition of acetic acid, using methanol as a solvent significantly affected the reactivity. In fact, as presented in Table 1, the addition of catalytic amounts of acetic acid allows a complete conversion of the reactant in 60 min. It should be noted that, on the contrary, conducting a reaction in a mixture of acetic acid and methanol (1:1) reduces the reactivity of the reagents and leads to the formation of several by-products.
Thus, it was discoveredthat the reaction between dimethylacetylenedicarboxylate 1 and 1,2-diamino-4-phenylimidazoles 44a-e proceeds most smoothly when methanol with the addition of a catalytic amount of acetic acid was used as solvent. In this case, the complete conversion of the starting diamine and the maximum yield of the target product were achieved after an hour of boiling the reagents.
Considering the polynucleophilic nature of the starting1,2-diaminoimidazoles 44a-e, Scheme 7 reports the structures of all possible intermediates of their interaction with DMAD 1. Thus, during the first step, the nucleophilic addition of 44a-e on the triple bond of1 due to the nucleophilic CH, NH, and NH2 groups, in addition to the nitrogen atom of the cycle, can lead to the formation of the intermediates A-D. The resulting Michael adducts can undergo intramolecular cyclization, due to the "near" or "far" carboxyl group, with the formation of the corresponding products 45-50. To gain information on the real course of the reaction, we have examined the 1 Н-NMR spectra of the products of reaction. We have observed that, in them, the characteristic CH signals of the imidazole ring fragment and of the amino group of the hydrazine fragment were absent; this observation allowed us to exclude the possibility that compounds 49 and 50 were formed. A further confirmation of this hypothesis was derived from the presence of the amino group signals at C-7 (6). Moreover, the spectra of the isolated compounds contained signals of the protons of the pyridazine ring at δ = To gain information on the real course of the reaction, we have examined the 1 H-NMR spectra of the products of reaction. We have observed that, in them, the characteristic CH signals of the imidazole ring fragment and of the amino group of the hydrazine fragment were absent; this observation allowed us to exclude the possibility that compounds 49 and 50 were formed. A further confirmation of this hypothesis was derived from the presence of the amino group signals at C-7 (6). Moreover, the spectra of the isolated compounds contained signals of the protons of the pyridazine ring at δ = 5.9-6.3 ppm, while the spectra of compound 45a, in which R was a hydrogen atom, contained the characteristic signal of the amide proton at δ = 11.75 ppm. Thus, it was possible to also exclude the structures 46 and 48. At this point, we can confirmthat only the structures 45 and 47 are possible for the obtained products of reaction.
The key criterion for choosing between these two structures (45 and 47) was the presence of cross peaks in the NOESY spectrum between the protons of the methyl group of the ester fragment and the ortho-protons of the aromatic ring present on C-5 of the imidazole ring, as presentedin Figure 1 for compound 45b. Thus, we can conclude that the reaction of1,2-diaminoimidazoles 44a-e with DMAD produces the methyl esters of 7-amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylic acids 45a-e.
Molecules 2022, 27, x FOR PEER REVIEW 7 of 21 5.9-6.3 ppm, while the spectra of compound 45a, in which R was a hydrogen atom, contained the characteristic signal of the amide proton at δ = 11.75 ppm. Thus, it was possible to also exclude the structures 46 and 48. At this point, we can confirmthat only the structures 45 and 47 are possible for the obtained products of reaction.
The key criterion for choosing between these two structures (45 and 47) was the presence of cross peaks in the NOESY spectrum between the protons of the methyl group of the ester fragment and the ortho-protons of the aromatic ring present on C-5 of the imidazole ring, as presentedin Figure 1 for compound 45b. Thus, we can conclude that the reaction of1,2-diaminoimidazoles 44a-e with DMAD produces the methyl esters of 7-amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylic acids 45a-e. Of course, the structures of all the obtained compounds (45a-e) have been confirmed by the collected spectroscopic data ( 1 Н-and 13 C-NMR, in addition to HRMS data). All of the examined reactions occurred with good/excellent yields (68-89%).
To obtainan additional confirmation of the structure of the obtained imidazopyridazines 45a-e and as a further step of our research, we have carried out the transformation of methyl  The structure of imidazopyridazine 52 was also confirmed by the NOESY spectrum, in which cross-interaction between the CH proton of the pyridazine ring and or- Of course, the structures of all the obtained compounds (45a-e) have been confirmed by the collected spectroscopic data ( 1 H-and 13 C-NMR, in addition to HRMS data). All of the examined reactions occurred with good/excellent yields (68-89%).
To obtainan additional confirmation of the structure of the obtained imidazopyridazines 45a-e and as a further step of our research, we have carried out the transformation of methyl 7-amino-1,2-dihydro-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylate 45a into 7-amino-5-phenylimidazo[1,5-b]pyridazin-2-one 52 (Scheme 8). Thus, by alkaline hydrolysis 45a producedthe relevant carboxylic acid 51, which, in turn, by refluxing in diphenyl ether in the presence of copper acetate, furnished by decarboxylation (pathway A) the 7-amino-5-phenylimidazo[1,5-b]pyridazin-2-one 52. The structure of isolated compounds 51 and 52 was proven by 1 H-and 13 C-NMR spectroscopy and HRMS. 5.9-6.3 ppm, while the spectra of compound 45a, in which R was a hydrogen atom, contained the characteristic signal of the amide proton at δ = 11.75 ppm. Thus, it was possible to also exclude the structures 46 and 48. At this point, we can confirmthat only the structures 45 and 47 are possible for the obtained products of reaction.
The key criterion for choosing between these two structures (45 and 47) was the presence of cross peaks in the NOESY spectrum between the protons of the methyl group of the ester fragment and the ortho-protons of the aromatic ring present on C-5 of the imidazole ring, as presentedin Figure 1 for compound 45b. Thus, we can conclude that the reaction of1,2-diaminoimidazoles 44a-e with DMAD produces the methyl esters of 7-amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylic acids 45a-e. Of course, the structures of all the obtained compounds (45a-e) have been confirmed by the collected spectroscopic data ( 1 Н-and 13 C-NMR, in addition to HRMS data). All of the examined reactions occurred with good/excellent yields (68-89%).
To obtainan additional confirmation of the structure of the obtained imidazopyridazines 45a-e and as a further step of our research, we have carried out the transformation of methyl 7-amino-1,2-dihydro-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylate 45a into 7-amino-5-phenylimidazo[1,5-b]pyridazin-2-one 52 (Scheme 8). Thus, by alkaline hydrolysis 45a producedthe relevant carboxylic acid 51, which, in turn, by refluxing in diphenyl ether in the presence of copper acetate, furnished by decarboxylation (pathway A) the 7-amino-5-phenylimidazo[1,5-b]pyridazin-2-one 52. The structure of isolated compounds 51 and 52 was proven by 1 Н-and 13 С-NMR spectroscopy and HRMS. The structure of imidazopyridazine 52 was also confirmed by the NOESY spectrum, in which cross-interaction between the CH proton of the pyridazine ring and or- The structure of imidazopyridazine 52 was also confirmed by the NOESY spectrum, in which cross-interaction between the CH proton of the pyridazine ring and ortho-protons of the aromatic ring was observed (Figure 2). This kind of interaction is impossible for this couple of protons in all alternative structures 46-48. Therefore, the proven structure of imidazopyridazine 52 has further confirmed that in the course of the interaction between 1,2-diaminoimidazoles 44a-e and DMAD, methyl esters of 7-amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylic acids 45a-e have been obtained. tho-protons of the aromatic ring was observed (Figure 2). This kind of interaction is impossible for this couple of protons in all alternative structures 46-48. Therefore, the proven structure of imidazopyridazine 52 has further confirmed that in the course of the interaction between 1,2-diaminoimidazoles 44a-e and DMAD, methyl esters of 7-amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylic acids 45a-e have been obtained. The structure of compound 52 was further confirmed by preparing it with an alternative synthesis, id est by treating the 1,2-diamino-4-phenylimidazole 44a with ethyl propargylate 53 (Scheme 8, pathway B). As in the instance of the reaction with DMAD, the optimal condition was boiling for 60 min the mixture of reagents in methanol with the addition of a couple of drops of acetic acid under constant stirring.
To obtainfurther information on the course of the reaction between 1,2-diaminoimidazoles 44 and DMAD 1, we have calculated the minimum energy paths (MEP) for the reaction. Quantum-chemical DFT calculations were performed using B3LYP/6-311++G(d, p) basis and considering the solvation effects by the polarizable continuum model (PCM) in methanol.
In the first step of this process, anucleophilic attack of carbon atom С-5 of imidazole on a carbon atom of the triple bond of DMAD 1occurred with the formation of the bipolar σ-complex 54, which was 23.3 kcal/mol higher in energy comparedto the starting reagents ( Figure 3). The structure of compound 52 was further confirmed by preparing it with an alternative synthesis, id est by treating the 1,2-diamino-4-phenylimidazole 44a with ethyl propargylate 53 (Scheme 8, pathway B). As in the instance of the reaction with DMAD, the optimal condition was boiling for 60 min the mixture of reagents in methanol with the addition of a couple of drops of acetic acid under constant stirring.
To obtainfurther information on the course of the reaction between 1,2-diaminoimidazoles 44 and DMAD 1, we have calculated the minimum energy paths (MEP) for the reaction. Quantum-chemical DFT calculations were performed using B3LYP/6-311++G(d, p) basis and considering the solvation effects by the polarizable continuum model (PCM) in methanol.
In the first step of this process, anucleophilic attack of carbon atom C-5 of imidazole on a carbon atom of the triple bond of DMAD 1 occurred with the formation of the bipolar σ-complex 54, which was 23.3 kcal/mol higher in energy comparedto the starting reagents ( Figure 3). tho-protons of the aromatic ring was observed (Figure 2). This kind of interaction is impossible for this couple of protons in all alternative structures 46-48. Therefore, the proven structure of imidazopyridazine 52 has further confirmed that in the course of the interaction between 1,2-diaminoimidazoles 44a-e and DMAD, methyl esters of 7-amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylic acids 45a-e have been obtained. The structure of compound 52 was further confirmed by preparing it with an alternative synthesis, id est by treating the 1,2-diamino-4-phenylimidazole 44a with ethyl propargylate 53 (Scheme 8, pathway B). As in the instance of the reaction with DMAD, the optimal condition was boiling for 60 min the mixture of reagents in methanol with the addition of a couple of drops of acetic acid under constant stirring.
To obtainfurther information on the course of the reaction between 1,2-diaminoimidazoles 44 and DMAD 1, we have calculated the minimum energy paths (MEP) for the reaction. Quantum-chemical DFT calculations were performed using B3LYP/6-311++G(d, p) basis and considering the solvation effects by the polarizable continuum model (PCM) in methanol.
In the first step of this process, anucleophilic attack of carbon atom С-5 of imidazole on a carbon atom of the triple bond of DMAD 1occurred with the formation of the bipolar σ-complex 54, which was 23.3 kcal/mol higher in energy comparedto the starting reagents ( Figure 3). Now we will discuss the change in the relative free energy ∆G. During the second step of the process, a 1,3-hydrogen shift occurred and the covalent σ-complex 55 was formed: although the formation of this structure required an activation energy of 21.0 kcal/mol, 55 is produced, which is much more stable. In the final step, an intramolecular nucleophilic attack by the nitrogen atom of the amino group on the carbonyl carbon atom occurred, followed by the elimination of the methanol molecule and the formation of the final product 45a. The formation of 45a was highly exothermic (a gain of 30.6 kcal/mol occurred), and it required the overcoming of a very large energy barrier (45.5 kcal/mol) in the last step (TS3) (Scheme 9). Now we will discuss the change in the relative free energy ΔG. During the second step of the process, a 1,3-hydrogen shift occurred and the covalent σ-complex 55 was formed: although the formation of this structure required an activation energy of 21.0 kcal/mol, 55 is produced, which is much more stable. In the final step, an intramolecular nucleophilic attack by the nitrogen atom of the amino group on the carbonyl carbon atom occurred, followed by the elimination of the methanol molecule and the formation of the final product 45a. The formation of 45a was highly exothermic (a gain of 30.6 kcal/mol occurred), and it required the overcoming of a very large energy barrier (45.5 kcal/mol) in the last step (TS3) (Scheme 9). Scheme 9. Proposed bimolecular formation mechanism of 45а.
Then we considered the reaction proceeded via the intermediate D, theoretically leading to the formation of product 50-2 (Schemes 7 and 10). During the first step of the studied process, a nucleophilic attack by N-3 of imidazole on a carbon atom of the triple bond of DMAD 1 occurred with the formation of the bipolar σ-complex 56. As in the previous instance, the formation of a non-classical structure is energetically unfavorable; in fact, structure 56 was 20.2 kcal/mol higher in energy than the initial reagents ( Figure 4). During the second step, a 1,5-hydrogen shift occurred and the compound 57 was formed. It should be noted that 57 appears to be the final product; in fact, further cyclization into product 50-2 was not observed. In general, this path was weakly endothermic: 57 was energetically less favorable than the initial reagents, then the formation of complex D was unlikely. Scheme 9. Proposed bimolecular formation mechanism of 45a.
Then we considered the reaction proceeded via the intermediate D, theoretically leading to the formation of product 50-2 (Schemes 7 and 10). Now we will discuss the change in the relative free energy ΔG. During the second step of the process, a 1,3-hydrogen shift occurred and the covalent σ-complex 55 was formed: although the formation of this structure required an activation energy of 21.0 kcal/mol, 55 is produced, which is much more stable. In the final step, an intramolecular nucleophilic attack by the nitrogen atom of the amino group on the carbonyl carbon atom occurred, followed by the elimination of the methanol molecule and the formation of the final product 45a. The formation of 45a was highly exothermic (a gain of 30.6 kcal/mol occurred), and it required the overcoming of a very large energy barrier (45.5 kcal/mol) in the last step (TS3) (Scheme 9). Scheme 9. Proposed bimolecular formation mechanism of 45а.
Then we considered the reaction proceeded via the intermediate D, theoretically leading to the formation of product 50-2 (Schemes 7 and 10). During the first step of the studied process, a nucleophilic attack by N-3 of imidazole on a carbon atom of the triple bond of DMAD 1 occurred with the formation of the bipolar σ-complex 56. As in the previous instance, the formation of a non-classical structure is energetically unfavorable; in fact, structure 56 was 20.2 kcal/mol higher in energy than the initial reagents ( Figure 4). During the second step, a 1,5-hydrogen shift occurred and the compound 57 was formed. It should be noted that 57 appears to be the final product; in fact, further cyclization into product 50-2 was not observed. In general, this path was weakly endothermic: 57 was energetically less favorable than the initial reagents, then the formation of complex D was unlikely. During the first step of the studied process, a nucleophilic attack by N-3 of imidazole on a carbon atom of the triple bond of DMAD 1 occurred with the formation of the bipolar σ-complex 56. As in the previous instance, the formation of a non-classical structure is energetically unfavorable; in fact, structure 56 was 20.2 kcal/mol higher in energy than the initial reagents ( Figure 4). During the second step, a 1,5-hydrogen shift occurred and the compound 57 was formed. It should be noted that 57 appears to be the final product; in fact, further cyclization into product 50-2 was not observed. In general, this path was weakly endothermic: 57 was energetically less favorable than the initial reagents, then the formation of complex D was unlikely. Now the formation of a complex of type С (leading to products 49-2 or 50-1) will be examined (Schemes 7 and 11). Scheme 11. Proposed bimolecular formation mechanism of 59. Now, during the first step of the reaction, anucleophilic attack of the nitrogen atom of the amino group linked at the C-2 atom of imidazole occurred on a carbon atom of the triple bond of DMAD 1 with the formation of the bipolar σ-complex 58: it was 33.4 kcal higher in energy than the starting reagents ( Figure 5). The following 1,3-hydrogen shift led to the formation of the covalent adduct 59. However, as in the previously examined process (Scheme 10), the following cyclization into products 49-2 or 50-1 did not exist on the potential energy surface (PES).   Now the formation of a complex of type С (leading to products 49-2 or 50-1) will be examined (Schemes 7 and 11). Scheme 11. Proposed bimolecular formation mechanism of 59. Now, during the first step of the reaction, anucleophilic attack of the nitrogen atom of the amino group linked at the C-2 atom of imidazole occurred on a carbon atom of the triple bond of DMAD 1 with the formation of the bipolar σ-complex 58: it was 33.4 kcal higher in energy than the starting reagents ( Figure 5). The following 1,3-hydrogen shift led to the formation of the covalent adduct 59. However, as in the previously examined process (Scheme 10), the following cyclization into products 49-2 or 50-1 did not exist on the potential energy surface (PES). Scheme 11. Proposed bimolecular formation mechanism of 59. Now, during the first step of the reaction, anucleophilic attack of the nitrogen atom of the amino group linked at the C-2 atom of imidazole occurred on a carbon atom of the triple bond of DMAD 1 with the formation of the bipolar σ-complex 58: it was 33.4 kcal higher in energy than the starting reagents ( Figure 5). The following 1,3-hydrogen shift led to the formation of the covalent adduct 59. However, as in the previously examined process (Scheme 10), the following cyclization into products 49-2 or 50-1 did not exist on the potential energy surface (PES). The processes involving the formation of type B complexes proceeded through the formation of a bipolar σ-complex. Zwitterionic adduct 60 was formed by the nucleophilic attack of theN-amino group of imidazole 44a on a carbon atom of the triple bond of DMAD 1 (Scheme 12), then giving the covalent adduct 61 as a result of the 1,3-hydrogen shift. The formation of adduct 61 from DMDA 1 and 44 was energetically favorable and was accompanied by an energy gain of 17.3 kcal/mol ( Figure 6). The maximum barrier of the process 1 + 44→61 concerns the first stage (TS8) and required an activation energy of 38.2 kcal/mol. As in the two previous cases, the formation of a cyclic structure from adduct 61 was not suggested by PES.  The processes involving the formation of type B complexes proceeded through the formation of a bipolar σ-complex. Zwitterionic adduct 60 was formed by the nucleophilic attack of the N-amino group of imidazole 44a on a carbon atom of the triple bond of DMAD 1 (Scheme 12), then giving the covalent adduct 61 as a result of the 1,3-hydrogen shift. The formation of adduct 61 from DMDA 1 and 44 was energetically favorable and was accompanied by an energy gain of 17.3 kcal/mol ( Figure 6). The maximum barrier of the process 1 + 44→61 concerns the first stage (TS8) and required an activation energy of 38.2 kcal/mol. As in the two previous cases, the formation of a cyclic structure from adduct 61 was not suggested by PES. The processes involving the formation of type B complexes proceeded through the formation of a bipolar σ-complex. Zwitterionic adduct 60 was formed by the nucleophilic attack of theN-amino group of imidazole 44a on a carbon atom of the triple bond of DMAD 1 (Scheme 12), then giving the covalent adduct 61 as a result of the 1,3-hydrogen shift. The formation of adduct 61 from DMDA 1 and 44 was energetically favorable and was accompanied by an energy gain of 17.3 kcal/mol ( Figure 6). The maximum barrier of the process 1 + 44→61 concerns the first stage (TS8) and required an activation energy of 38.2 kcal/mol. As in the two previous cases, the formation of a cyclic structure from adduct 61 was not suggested by PES.  In conclusion, calculations for the bimolecular pathways of interaction of 4-phenyl-1H-imidazole-1,2-diamine 44a and DMAD 1indicatedthat between the hypothetical cyclic products 45-50, only the formation of a cyclic system 45а appeared as a possible path of reaction.In addition, data of quantum-chemical calculations on the course of the bimolecular processes indicatedthat the open-chain covalent adducts 59 and 61 could be formed, but their formation occurred with an energy barrier in the first stage higher than in the instance of the formation of adduct 54.
Since, according to the results of the experiments carried out using an alcohol as solvent of reaction, re-esterification products were recorded, we concludedthat the interaction of 4-phenyl-1H-imidazole-1,2-diamine 44a and DMAD 1 can develop not only via a bimolecular process, but also as a trimolecular process with the involvement of an alcohol molecule. For this, we performed the quantum-chemical calculation of paths involving methanol.
Firstly, we have considered the trimolecular process concerning the formation of the target product 45a (Scheme 13, Figure 7). At the molecular level, the methanol molecule affects all steps of the process. Thus, in the first step, during the formation of the bipolar σ-complex 62, the proton of the hydroxyl of methanol was coordinated to the carbon atom charged negatively inthe multiple bond. However, no stabilization of the zwitterionic structure (compared with the process on Scheme 9) occurred; in fact, the adduct 62 was less energy-efficient by 27.1 kcal/mol compared to the starting reagents. Furthermore, the lowbarrier of the 1,3-hydrogen shift which led to 63 was performed through a five-center transition state (TS11), in which the molecule of methanol acted as a bifunctional catalyst. In conclusion, calculations for the bimolecular pathways of interaction of 4-phenyl-1H-imidazole-1,2-diamine 44a and DMAD 1 indicatedthat between the hypothetical cyclic products 45-50, only the formation of a cyclic system 45a appeared as a possible path of reaction. In addition, data of quantum-chemical calculations on the course of the bimolecular processes indicatedthat the open-chain covalent adducts 59 and 61 could be formed, but their formation occurred with an energy barrier in the first stage higher than in the instance of the formation of adduct 54.
Since, according to the results of the experiments carried out using an alcohol as solvent of reaction, re-esterification products were recorded, we concludedthat the interaction of 4-phenyl-1H-imidazole-1,2-diamine 44a and DMAD 1 can develop not only via a bimolecular process, but also as a trimolecular process with the involvement of an alcohol molecule. For this, we performed the quantum-chemical calculation of paths involving methanol.
Firstly, we have considered the trimolecular process concerning the formation of the target product 45a (Scheme 13, Figure 7). At the molecular level, the methanol molecule affects all steps of the process. Thus, in the first step, during the formation of the bipolar σ-complex 62, the proton of the hydroxyl of methanol was coordinated to the carbon atom charged negatively inthe multiple bond. However, no stabilization of the zwitterionic structure (compared with the process on Scheme 9) occurred; in fact, the adduct 62 was less energy-efficient by 27.1 kcal/mol compared to the starting reagents. Furthermore, the lowbarrier of the 1,3-hydrogen shift which led to 63 was performed through a five-center transition state (TS11), in which the molecule of methanol acted as a bifunctional catalyst. Finally, the covalent 63 was transformed into product 45a through the transition state TS12, in which the molecule of methanol again performed the function of a bifunctional catalyst and participated in the formal transfer of a proton from the N-amino group to the ester oxygen atom. Despite the participation of the methanol in the proton transfer, the formation of product 45a from 63 proceeded with a barrier of 48.2 kcal/mol, which was higher than in the process portrayedin Scheme 9. Finally, the covalent 63 was transformed into product 45a through the transition state TS12, in which the molecule of methanol again performed the function of a bifunctional catalyst and participated in the formal transfer of a proton from the N-amino group to the ester oxygen atom. Despite the participation of the methanol in the proton transfer, the formation of product 45a from 63 proceeded with a barrier of 48.2 kcal/mol, which was higher than in the process portrayedin Scheme 9.  Finally, the covalent 63 was transformed into product 45a through the transition state TS12, in which the molecule of methanol again performed the function of a bifunctional catalyst and participated in the formal transfer of a proton from the N-amino group to the ester oxygen atom. Despite the participation of the methanol in the proton transfer, the formation of product 45a from 63 proceeded with a barrier of 48.2 kcal/mol, which was higher than in the process portrayedin Scheme 9.
The addition of a methanol molecule in the process presented in Scheme 10 causes an effect at the molecular level (Scheme 14). Thus, when the bipolar intermediate 64 was formed from the initial reagents, the methanol coordinated the proton of the hydroxy group to the carbon atom of the double bond. The addition of a methanol molecule in the process presented in Scheme 10 causes an effect at the molecular level (Scheme 14). Thus, when the bipolar intermediate 64 was formed from the initial reagents, the methanol coordinated the proton of the hydroxy group to the carbon atom of the double bond.
Despite the coordination of the zwitterionic 56 with a molecule of methanol in complex 64, this was 28.1 kcal/mol higher in energy than the initial reagents, which in turn means 7.9 kcal/mol higher in energy than for 56 in Scheme 10 (compare Figures 4 and 8). Despite the coordination of the zwitterionic 56 with a molecule of methanol in complex 64, this was 28.1 kcal/mol higher in energy than the initial reagents, which in turn means 7.9 kcal/mol higher in energy than for 56 in Scheme 10 (compare Figures 4 and 8). The addition of a methanol molecule in the process presented in Scheme 10 causes an effect at the molecular level (Scheme 14). Thus, when the bipolar intermediate 64 was formed from the initial reagents, the methanol coordinated the proton of the hydroxy group to the carbon atom of the double bond.
Despite the coordination of the zwitterionic 56 with a molecule of methanol in complex 64, this was 28.1 kcal/mol higher in energy than the initial reagents, which in turn means 7.9 kcal/mol higher in energy than for 56 in Scheme 10 (compare Figures 4 and 8).  The methanol molecule facilitated the 1,5-proton transfer, being included in the eighthcenter transition state (TS14), performing the function of a bifunctional catalyst. As before, the process of the formation of structure 57 was endothermic.
When the methanol molecule was involved in the processes reported in Schemes 11 and 12, we observed a similar pattern (see Supplementary Materials). It was coordinated with the zwitterion, destabilizing it. However, during the following step of the process, the methanol acted as a bifunctional catalyst facilitating the transfer of the hydrogen atom. In this case, the reactions, as in the case of the bimolecular pathway, stop at the stage of the formation of the covalent adducts.
According to the calculation data, a pattern analogous to the trimolecular processes with the involvement of methanol was observed in the case of the participation of acetic acid in the trimolecular process at the molecular level. Thus, for the process of formation of the compound 45a from the initial compounds, the barrier of the first stage of the formation of the zwitterionic associate was 40.4 kcal/mol, and the zwitterionic associate itself was 26.3 kcal/mol higher in energy than the initial reagents. The covalent adduct into which it rearranged, as a result of electron transfer, was 9.0 kcal/mol higher in energy comparedto the starting reagents. The trimolecular process with the involvement of acetic acid, as in the case of the participation of methanol, TS was higher in energy than in the corresponding bimolecular processes. Obviously, in all the cases considered, the involvement of a polar protic solvent at the molecular level can make worse the course of reactions. However, the covalent and zwitterionic intermediates in trimolecular processes were higher in energy than the intermediates infinitely separated from the solvent molecules, which means that the reaction can proceed by bimolecular pathways without switching to the trimolecular ones. Then, the experimentally observed ease of processes in polar solvents is explained exclusively by the dielectric constant (polarity of the medium). In fact, the higher the polarity of the medium, the higher the stabilizationenergy of zwitterionic or ionic processes [46].
When switching from the gas-phase calculations to the PCM medium accounting for the process in Scheme 9, we observed a reduction in the barrier values. Thus, the barrier of the first stage (TS1) is only 27 kcal/mol (see Supporting Materials) and the thermodynamic gain of the whole process increased to 39.3 kcal/mol.
Thus, based on quantum chemical calculations, the following conclusions can be drawn: the predominant cyclic product of the interaction of diaminoimidazoles 44 with DMAD 1 is imidazopyridazines 45; -open-chain nucleophilic addition products of diaminoimidazoles 44 to DMAD 1 at positions other than the C-2 carbon atom, which are less preferable kinetically, can participate in a further cascade of processes leading to the formation of difficultly separable mixtures not involved in further intramolecular cyclization; -interaction of diaminoimidazoles 44 with DMAD 1 is complicated in the instance that methanol or acetic acid participate to the reaction. In fact, the participation of the molecules of the third component in the formation of the primary bipolar σ-complexes can destabilize them. Conversely, during the following steps of the process, they can facilitate the transfer of protons because of the formation of classical covalent adducts; -the fact that all stationary points in the instance of trimolecular processes are higher in energy than the sum energies of the corresponding points and solvent molecules in case of bimolecular processes makes trimolecular processes alternative, but not real, processes. -polar solvents can facilitate the formation processes of type 45 systems due to their polarity (ε value), stabilizing polar intermediates, and not due to their direct involvement in the processes.  40), then for 5 min to 90% CH 3 CN), column-Poroshell 120 EC-C18 (4.6 × 50 mm, 2.7 µm), thermostat 23-28 • C, flow rate of 0.3-0.4 mL/min electrospray ionization (capillary-3.5 kV; fragmentor +191 V; OctRF +66 V-positive polarity). The course of the reaction and the purity of the obtained compounds were controlled by TLC on Merck TLC Silica gel 60 F254 plates in a 20:1 CHCl 3 -MeOH system (visualization under UV light). The commercially available reagents were purchased from Acros Organics (Geel, Belgium).

Materials and Methods
Quantum chemical DFT calculations were carried out in the 6-311++G(d,p) triple-zeta basis using a B3LYP functional [47]. This basis has provideda good account of itself in reproduction of vibrational frequencies, geometry, and minimum energy reaction paths [48][49][50]. Full geometry optimization of molecular structures corresponding to stationary points of the potential energy surface was carried out as high as a gradient value of 10 −7 hartree/bohr according to the Gaussian 09 software package (Wallingford, CT, USA) [51] using the Silver cluster of the Research Institute of Physical and Organic Chemistry at SFedU. The nature of stationary points was determined relying on the calculation of normal vibration frequencies (the Hessian matrix). MEPs were plotted using gradient descent from transition states in forward and reverse directions of transition vectors. In order to search for transition states, linear and quadratic synchronous transit methods were used [52,53].

General
Procedure for the Synthesis of Methyl 7-Amino-1,2-dihydro-1-R-2-oxo-5-phenylimidazo[1,5-b]pyridazine-4-carboxylates (45a-e) Acetylene dicarboxylic acid dimethyl ester 1 (5 mmol) was added dropwise to 5 mmol of diaminoimidazole 44a-e dissolved in 5 mLof methanol containing catalytic amounts of acetic acid (2-3 drops). After adding 1, the reaction mixture was refluxed for 60 min. The precipitated crystals were filtered off and recrystallized from MeOH. diates. The use of a protic solvent (methanol and few drops of acetic acid) accelerates the course of the processes; this factis probably not due to their involvement as catalysts, but to a change in the dielectric constant of the medium, able to stabilizepolar intermediates. DFT results confirm the experimental results, moreover, the observed course of the reaction (formation of compounds 45a-e) is confirmed by spectroscopic results.