Mechanistic DFT Study of 1,3-Dipolar Cycloadditions of Azides with Guanidine

Density functional calculations SMD(chloroform)//B3LYP/6-311+G(2d,p) were employed in the computational study of 1,3-dipolar cycloadditions of azides with guanidine. The formation of two regioisomeric tetrazoles and their rearrangement to cyclic aziridines and open-chain guanidine products were modeled. The results suggest the feasibility of an uncatalyzed reaction under very drastic conditions since the thermodynamically preferred reaction path (a), which involves cycloaddition by binding the carbon atom from guanidine to the terminal azide nitrogen atom, and the guanidine imino nitrogen with the inner N atom from the azide, has an energy barrier higher than 50 kcal mol−1. The formation of the other regioisomeric tetrazole (imino nitrogen interacts with terminal N atom of azide) in direction (b) can be more favorable and proceed under milder conditions if alternative activation of the nitrogen molecule releases (e.g., photochemical activation), or deamination could be achieved because these processes have the highest barrier in the less favorable (b) branch of the mechanism. The introduction of substituents should favorably affect the cycloaddition reactivity of the azides, with the greatest effects expected for the benzyl and perfluorophenyl groups.


Introduction
Guanidines are organic compounds that possess very interesting physico-chemical properties, such as very high basicity [1,2] and biological activity [3]. Their chemical behavior is extensively studied and guanidines have found applications in various fields, such as catalysis [4], coordination chemistry [5], supramolecular chemistry [6], medicinal chemistry [7,8] and chemical sensoring [9,10]. Whereas this versatile functional group undergoes numerous chemical reactions, guanidines are rarely involved in cycloaddition reactions [11], either in Diels-Alder or dipolar cycloadditions. Moreover, there are scarce reports on the cycloadditions where the imino bond of guanidines undertakes the role of dipolarophile with the formation of a new heterocyclic ring. An example is the formal 1,3-dipolar cycloaddition to guanidine, where aryldiazonium salts reacted with guanidines [12], NIS/DBU catalyzed to obtain aminotetrazoles-a multistep process involving nucleophilic addition/cyclization. The mechanistically similar formal 1,3-dipolar reaction of aryldiazonium salts and amidines facilitated by K 2 CO 3 /I 2 provided tetrazole [13]. Tetrazoles are of great interest due to their various biological activities [14], and are constituents of many active pharmaceutical ingredients [15].
Different synthetic strategies are employed for the synthesis of tetrazoles [16]; however, the direct addition of azide to guanidine was not utilized. Realizing that this type of reaction has not been not theoretically studied to date, and in continuation of our interest in cycloaddition reactions [17,18] and study of the effects of the substitution of dienes with guanidines [19], we conducted this computational study to address several scientific questions: What is the reactivity of guanidine in 1,3-dipolar cycloadditions, and what is the regioselectivity of this reaction? This study aims to establish the cycloaddition (dipolarophilic) properties of imine bond in guanidine and the regioselectivity of the The theoretical study of the reaction mechanism of the 1,3-dipolar cycload azide to the guanidine C=N double bond was initiated w SMD(chloroform)//B3LYP/6-311+G(2d,p) calculations of unsubstituted derivativ AZ1 (hydrazoic acid) and guanidine GU (Figure 2). The B3LYP functional [2 previously used for successful regioselectivity investigations of similar uncatalyzed 1,3-dipolar cycloadditions [22][23][24][25], including azide cycloadd acetylenes [26]; and azide cycloaddition to nitriles forming tetrazoles [27], which applications of DFT methods to this kind of reaction. The theoretical study of the reaction mechanism of the 1,3-dipolar cycloaddition of azide to the guanidine C=N double bond was initiated with the SMD(chloroform)//B3LYP/6-311+G(2d,p) calculations of unsubstituted derivatives: azide AZ1 (hydrazoic acid) and guanidine GU (Figure 2). The B3LYP functional [20,21] was previously used for successful regioselectivity investigations of similar thermal, uncatalyzed 1,3-dipolar cycloadditions [22][23][24][25], including azide cycloaddition to acetylenes [26]; and azide cycloaddition to nitriles forming tetrazoles [27], which are early applications of DFT methods to this kind of reaction.
The addition of an azide functional group to a C=N double bond can proceed in two ways, leading to two different regioisomers: (a) the carbon atom from guanidine binds to the terminal azide N3 atom, and the guanidine imino nitrogen interacts with the N1 atom from the azide; in the second reaction mode (b), interacting atoms are reversed. Imino nitrogen (N4) forms a bond to the N3 end of the azide group while the carbon atom interacts with the N1 azide nitrogen. In both regioisomeric approaches, the formation of new C-N and N-N bonds is a concerted process, but due to the asymmetry of the reagents, the transition structures are partly asymmetric ( Figure 2). The bond lengths of new forming bonds are in good accordance with the reactions of azides to enamines [28], alkenes (distances 2.02-2.27 Å) [29], or to nitriles (distances 1.92-2.07 Å; regioisomers' energy difference is smaller-∆∆H act is about 5-6 kcal mol −1 ) [27]. The addition of an azide functional group to a C=N double bond can procee ways, leading to two different regioisomers: (a) the carbon atom from guanidine the terminal azide N3 atom, and the guanidine imino nitrogen interacts with the N from the azide; in the second reaction mode (b), interacting atoms are reversed nitrogen (N4) forms a bond to the N3 end of the azide group while the carbo interacts with the N1 azide nitrogen. In both regioisomeric approaches, the form new C-N and N-N bonds is a concerted process, but due to the asymmetry of the r the transition structures are partly asymmetric ( Figure 2). The bond lengths forming bonds are in good accordance with the reactions of azides to enamin alkenes (distances 2.02-2.27 Å) [29], or to nitriles (distances 1.92-2.07 Å; regio energy difference is smaller-ΔΔHact is about 5-6 kcal mol −1 ) [27].
The direction (b) is energetically significantly more favorable, by 18.3 kcal m (1TS1b) = 35.9 kcal mol −1 vs. Erel (1TS1a) = 54.2 kcal mol −1 ) ( Figure 3). Both proce endothermic and the 5,5-diamino-1,4(or 2)-dihydro-1,2,3,4-tetrazole products stable than the reactant by 26.2 and 17.2 kcal mol −1 for (a) and (b) directions of the r respectively. It is known that the triazolines formed by the analogous cycloadd azides to alkenes are unstable and convert to aziridines, amines, or pyrazolines [1 Hence, we assumed that in the case of additions to guanidine, the resulting t products would also be thermodynamically unstable and subject to rearrangements. Two transition state structures for the release of N2 and two TS st for the release of NH3 molecules were found on the potential energy surface. In direction, the release of N2 is far more probable than the release of ammonia bec energy barrier is extremely small, only 4.7 kcal mol −1 . The resulting diradical inter is even more easily rearranged to form thermodynamically stable amino-guanid products ( Figure 3). In the (b) reaction direction, the release of ammonia is favorable process than the release of N2, but it should be borne in mind that both p are significantly more energy-demanding than identical processes for direction (a The direction (b) is energetically significantly more favorable, by 18.3 kcal mol −1 (E rel (1TS1b) = 35.9 kcal mol −1 vs. E rel (1TS1a) = 54.2 kcal mol −1 ) ( Figure 3). Both processes are endothermic and the 5,5-diamino-1,4(or 2)-dihydro-1,2,3,4-tetrazole products are less stable than the reactant by 26.2 and 17.2 kcal mol −1 for (a) and (b) directions of the reaction, respectively. It is known that the triazolines formed by the analogous cycloaddition of azides to alkenes are unstable and convert to aziridines, amines, or pyrazolines [15,30,31]. Hence, we assumed that in the case of additions to guanidine, the resulting tetrazole products would also be thermodynamically unstable and subject to similar rearrangements. Two transition state structures for the release of N 2 and two TS structures for the release of NH 3 molecules were found on the potential energy surface. In the (a) direction, the release of N 2 is far more probable than the release of ammonia because the energy barrier is extremely small, only 4.7 kcal mol −1 . The resulting diradical intermediate is even more easily rearranged to form thermodynamically stable amino-guanidine end-products ( Figure 3). In the (b) reaction direction, the release of ammonia is a more favorable process than the release of N 2 , but it should be borne in mind that both processes are significantly more energy-demanding than identical processes for direction (a).
The effect on the reactivity of azide substitution obtained by different functional groups was examined by the introduction of methyl (AZ2), phenyl (AZ3), benzyl (AZ4), and perfluorophenyl (AZ5) groups to the azide functionality. The energy profiles of these reactions are given in Figures 4-7.
The replacement of the azide hydrogen atom with different functional groups did not lead to a significant change in the geometry of the TS structures for cycloaddition when the carbon atom approached the azide terminal N3 atom (a reaction direction) ( Figure 8). The synchronous cycloaddition process is energetically more favorable for 2.5-4.2 kcal mol −1 compared to hydrazoic acid AZ1. The lowest energy barrier was computed for the reaction of guanidine with AZ5 (introduction of the perfluorophenyl group). Additionally, the benzoyl group is preferable when compared to phenyl, which is in good accordance with the larger cycloaddition reactivity of benzyl compared to phenyl azide [32].               The replacement of the azide hydrogen atom with different functional groups did not lead to a significant change in the geometry of the TS structures for cycloaddition when the carbon atom approached the azide terminal N3 atom (a reaction direction) ( Figure 8). The synchronous cycloaddition process is energetically more favorable for 2.5-4.2 kcal mol −1 compared to hydrazoic acid AZ1. The lowest energy barrier was computed for the reaction of guanidine with AZ5 (introduction of the perfluorophenyl group). Additionally, the benzoyl group is preferable when compared to phenyl, which is in good accordance with the larger cycloaddition reactivity of benzyl compared to phenyl azide [32].    The replacement of the azide hydrogen atom with different functional groups did not lead to a significant change in the geometry of the TS structures for cycloaddition when the carbon atom approached the azide terminal N3 atom (a reaction direction) ( Figure 8). The synchronous cycloaddition process is energetically more favorable for 2.5-4.2 kcal mol −1 compared to hydrazoic acid AZ1. The lowest energy barrier was computed for the reaction of guanidine with AZ5 (introduction of the perfluorophenyl group). Additionally, the benzoyl group is preferable when compared to phenyl, which is in good accordance with the larger cycloaddition reactivity of benzyl compared to phenyl azide [32].   After cyclization, in all cases, the N 2 release and formation of stable products are expected. Activation energies for the elimination of N 2 are smaller for phenyl and C 6 F 5 substituents in comparison with an unsubstituted derivative (5.9 and 3.3 kcal mol −1 , respectively), whereas the substitution by methyl and benzyl raises the barrier (7.6 and 9.7 kcal mol −1 ). The activation energies for further diradical rearrangement are higher for phenyl and C 6 F 5 substituents (5.4 and 7.7 kcal mol −1 ) than for other substituents and could be associated with the better stabilization of aniline radicals [33]. Similar to unsubstituted reactants, the alternative process of deamination and amino-tetrazole ring formation is less favorable. For the deamination process, activation energies are in the range between 34.5 and 35.4 kcal mol −1 for all substituents, with the exception of phenyl, where E a is smaller than 33.1 kcal mol −1 .
There are some mechanistic differences in direction (b) in comparison to AZ1. The synchronous formation of N3-N4 and N1-C5 bonds occurs exclusively in the reaction of guanidine with phenylazide AZ3 (this is similar to AZ1). The relative energy of the transition structure is lower by 4.4 kcal mol −1 compared to the corresponding TS structure in the reaction of unsubstituted azide. The resulting adduct 1M3b is less stable than the unsubstituted adduct by 2.2 kcal mol −1 .
For other azides, AZ2, AZ4, and AZ5, the formation of diaminotetrazoles is a two-step process involving two TSs on the potential energy surface along the reaction pathway. The first (TSNb, N = 2,4,5) is a TS structure of a nucleophilic attack that creates a bond between the terminal azide nitrogen N3 and guanidine imino nitrogen N4 and the formation of intermediate 1MNb, N = 2,4,5. The activation energies for initial nucleophilic attack are significantly lower than for synchronous TS and the formation of diaminotetrazole, which indicates that the nucleophilicity properties of azides are increased by methyl, benzyl, and C 6 H 5 groups [34]. In the second stage of the reaction, the five-membered ring is closed by coupling the N1 azide nitrogen with a carbon atom from the guanidine group via a 1TSNb, N = 2,4,5 structures. Examples of such structures are shown for AZ2 in Figure 9.
substituents in comparison with an unsubstituted derivative (5.9 and 3.3 kcal mol − respectively), whereas the substitution by methyl and benzyl raises the barrier (7.6 an 9.7 kcal mol −1 ). The activation energies for further diradical rearrangement are higher fo phenyl and C6F5 substituents (5.4 and 7.7 kcal mol −1 ) than for other substituents and coul be associated with the better stabilization of aniline radicals [33]. Similar to unsubstitute reactants, the alternative process of deamination and amino-tetrazole ring formation i less favorable. For the deamination process, activation energies are in the range betwee 34.5 and 35.4 kcal mol −1 for all substituents, with the exception of phenyl, where Ea i smaller than 33.1 kcal mol −1 .
There are some mechanistic differences in direction (b) in comparison to AZ1. Th synchronous formation of N3-N4 and N1-C5 bonds occurs exclusively in the reaction o guanidine with phenylazide AZ3 (this is similar to AZ1). The relative energy of th transition structure is lower by 4.4 kcal mol −1 compared to the corresponding TS structur in the reaction of unsubstituted azide. The resulting adduct 1M3b is less stable than th unsubstituted adduct by 2.2 kcal mol −1 .
For other azides, AZ2, AZ4, and AZ5, the formation of diaminotetrazoles is a two step process involving two TSs on the potential energy surface along the reactio pathway. The first (TSNb, N = 2,4,5) is a TS structure of a nucleophilic attack that create a bond between the terminal azide nitrogen N3 and guanidine imino nitrogen N4 and th formation of intermediate 1MNb, N = 2,4,5. The activation energies for initial nucleophili attack are significantly lower than for synchronous TS and the formation o diaminotetrazole, which indicates that the nucleophilicity properties of azides ar increased by methyl, benzyl, and C6H5 groups [34]. In the second stage of the reaction, th five-membered ring is closed by coupling the N1 azide nitrogen with a carbon atom from the guanidine group via a 1TSNb, N = 2,4,5 structures. Examples of such structures ar shown for AZ2 in Figure 9. The nitrogen released from the formed diaminotetrazole adducts during the reactio path (b) goes through 3TS transition state structures with very high energies relative t the reactant: 67.1 (methyl group, 3TS2b), 62.9 (phenyl group, 3TS3b), 69.6 (benzyl group 3TS4b), and 60.6 kcal mol −1 (perfluorophenyl group 3TS5b). IRC calculations showed tha in the case of an adduct with a methyl group at the N1 position at the exit of N2, the amin group migrates from the C atom to the N1 position and a stable N',N aminomethylguanidine is formed (1P2b). In adducts with larger substituents (pheny benzyl, and parafluorophenyl), migration of the amino group was not observed, but th closure of the three-membered aziridine ring occurred ( Figure 10). The nitrogen released from the formed diaminotetrazole adducts during the reaction path (b) goes through 3TS transition state structures with very high energies relative to the reactant: 67.1 (methyl group, 3TS2b), 62.9 (phenyl group, 3TS3b), 69.6 (benzyl group, 3TS4b), and 60.6 kcal mol −1 (perfluorophenyl group 3TS5b). IRC calculations showed that in the case of an adduct with a methyl group at the N1 position at the exit of N 2 , the amino group migrates from the C atom to the N1 position and a stable N',N'-aminomethylguanidine is formed (1P2b). In adducts with larger substituents (phenyl, benzyl, and parafluorophenyl), migration of the amino group was not observed, but the closure of the three-membered aziridine ring occurred ( Figure 10).
The deamination of diaminotetrazole 2M structures goes through transition states 3TS before reaching the final product 2P (Figure 10). In the case of AZ1-AZ4, this process is kinetically more favorable than nitrogen release. It should be emphasized, however, that the energy barriers for this deamination (direction b) are also very high: 53.6 (-Me), 55.3 (-Ph), and 57.0 (-Bn). For AZ5, the energy of 3TS5b is 61.9 kcal mol −1 less favorable than the nitrogen release by 1.3 kcal mol −1 . The deamination of diaminotetrazole 2M structures goes through transition state 3TS before reaching the final product 2P (Figure 10). In the case of AZ1-AZ4, this proces is kinetically more favorable than nitrogen release. It should be emphasized, however that the energy barriers for this deamination (direction b) are also very high: 53.6 (-Me 55.3 (-Ph), and 57.0 (-Bn). For AZ5, the energy of 3TS5b is 61.9 kcal mol −1 less favorabl than the nitrogen release by 1.3 kcal mol −1 .
The effect of substitution on the guanidine moiety was investigated by observing th reaction of AZ4 with permethylated guanidine GU2. The energy profile is given in Figur  11. In brief, the cycloaddition part of the energy profile is very similar to that o unsubstituted guanidine (a comparison of energy profiles is provided in Figures 10 an  11), which means that the direction (a) is less favorable and energetically more demandin than direction (b). The energy barrier for cycloaddition in the (a) direction is almos identical in the case of GU and GU2. In the (b) direction, all stationary points have slightly lower energy in the case of GU2. The N2 release, similar to that found for GU, i more favorable in the (a) direction than the (b) direction. When the same behavior a before is observed in the (a) direction, a stable diradical intermediate is formed, which i further rearranged or cyclized into final products. The rearrangement is mor energetically demanding in the case of GU2, because the radical center needs to pick u Methyl instead of H, and more energy is needed for this. Cyclization results in a less stabl cyclic product, probably due to steric hindrance. The IRC calculation shows that, in th  The effect of substitution on the guanidine moiety was investigated by observing the reaction of AZ4 with permethylated guanidine GU2. The energy profile is given in Figure 11. In brief, the cycloaddition part of the energy profile is very similar to that of unsubstituted guanidine (a comparison of energy profiles is provided in Figures 10 and 11), which means that the direction (a) is less favorable and energetically more demanding than direction (b). The energy barrier for cycloaddition in the (a) direction is almost identical in the case of GU and GU2. In the (b) direction, all stationary points have a slightly lower energy in the case of GU2. The N 2 release, similar to that found for GU, is more favorable in the (a) direction than the (b) direction. When the same behavior as before is observed in the (a) direction, a stable diradical intermediate is formed, which is further rearranged or cyclized into final products. The rearrangement is more energetically demanding in the case of GU2, because the radical center needs to pick up Methyl instead of H, and more energy is needed for this. Cyclization results in a less stable cyclic product, probably due to steric hindrance. The IRC calculation shows that, in the (b) direction from the 2TS6b structure, the expected cyclic product 3P6b is not formed (we expected this because, in the case of GU, 3P5b was formed as a stable product). Instead, IRC leads to an intermediate structure for IM6b. An attempt to optimize this structure without an energy barrier leads to the final product, 1P6b (see Figure 12).
To summarize, the reaction energy profiles from this computational study indicate that the product of cycloaddition formed through direction (b) should be kinetically favored; however, further rearrangements (elimination) of initial cycloadducts can more easily energetically proceed through direction (a). Hence, the formation of aminoguanidine from direction (a) is a favorable process. To summarize, the reaction energy profiles from this computational study indicate that the product of cycloaddition formed through direction (b) should be kinetically favored; however, further rearrangements (elimination) of initial cycloadducts can more easily energetically proceed through direction (a). Hence, the formation of aminoguanidine from direction (a) is a favorable process.    To summarize, the reaction energy profiles from this computational study indicate that the product of cycloaddition formed through direction (b) should be kinetically favored; however, further rearrangements (elimination) of initial cycloadducts can more

Materials and Methods
The B3LYP/6-311+G(2d,p) method [18,19] was used to study the mechanism of azide addition to guanidine. Structures of reactants, transition states, and products were optimized without any symmetry constraints in the gas phase. Vibrational analysis was performed, and all structures were characterized either as minima without imaginary frequencies or as transition state structures with one imaginary frequency. The total energy of each stationary point on the surface of the potential energy was corrected by unscaled ZPV energy. The association of products with reactants via transition structures was confirmed by IRC calculations. All energy profiles are given in Figures S1-S6 in Supplementary Materials. To better mimic the usual experimental conditions, solvent effects were included as single-point calculations on optimized PES stationary points using the SMD method [35] and chloroform as solvent. Full population analysis with Hirshfeld [36,37] and the NBO [38] option was performed on reactants and selected TS structures. Partial atomic charges (Hirshfeld, NBO and Mulliken) of selected atoms are collected in Table S2. The Gaussian09 [39] software package was used to perform quantum-mechanical calculations, and the initial structures were generated using the Molden package [40].
Chloroform molecule is a very weak H-bonding acceptor and donor; therefore, strong explicit interactions with solute are not expected. Nevertheless, the calculations with one explicitly added CHCl 3 molecule were undertaken for the reaction of AZ3 with guanidine GU in the (a) direction. The results are listed in Supplementary Materials (Tables S3 and S5, Figure S7). It was shown that the energy profile was not altered when compared to previous results. Relative energies of all stationary points, with respect to reactants (TS as well as minima), were ca. 1.1-3.1 kcal mol −1 higher. It can be concluded that potential energy barriers were not substantially changed upon complexation with CHCl 3 molecule. There is no reason to expect that the effect of CHCl 3 complexation would be different for other azides studied in this paper.

Conclusions
The results of modeling the reaction pathways of the 1,3-dipolar cycloaddition of azides to guanidine suggest the feasibility of an uncatalyzed reaction, but under very drastic conditions. Regardless of the substituent that is present on azide, the formation of the aminoguanidine derivative by reaction path (a) is the thermodynamically most preferred process and, subject to high-temperature conditions, the expected product.
The reaction between azide and guanidine involves several steps, including the formation of different tetrazole intermediates and their rearrangements. It is interesting to note that the more favorable formation of the tetrazole intermediate is in the kinetically less favorable branch of the putative mechanism direction (b). This suggests the possibility of obtaining less thermodynamically favorable products under milder conditions but with alternative activation or release of the nitrogen molecule (e.g., photochemical activation) or deamination, because these processes have the highest barrier in the less favorable branch of the mechanism.
The introduction of azide substituents should favorably affect the cycloaddition reactivity of the azides, with the greatest effects being expected for the benzyl and perfluorophenyl groups.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28052342/s1, Figures S1-S6: Potential energy profiles for cycloadditions in the gas phase; Figure S7: Stationary points along the reaction path with solvent explicitly included; Tables S1-S3: Energies, selected partial atomic charges, charge analysis and coordinates of all structures associated with this article.