Investigations on the non-covalent interactions, drug-likeness, molecular docking and chemical properties of 1,1,4,7,7- pentamethyldiethylenetriammonium trinitrate by density-functional theory

2.1 Materials and measurements

The 1,1,4,7,7-pentamethyldiethylenetriammonium trinitrate (PMDT) single crystal 0.4 × 0.35 × 0.3 mm in size with a molecular weight of 362.36 g ∙ mol⁻¹ was investigated (Fig. 1a). The sample with the chemical formula C₉H₂₆N₆O₉ for the X-ray diffraction analysis had the form of a prism. The single-crystal X-ray analysis data on the PMDT compound were obtained on a CAD-4 EXPRESS diffractometer (Burkhardt et al., 1994) with a graphite monochromator (Ag Kα radiation, λ = 0.56083 Å) at 293 K. The structure was solved and refined in the SHELXS97 (Sheldrick, 2008) and SHELXL97 (Farrugia, 2012) software. The PMDT compound crystallizes in the triclinic centrosymmetric P $\overline{1}$ sp. gr. with lattice parameters of a = 5.964(2) Å, b = 7.018(1) Å, c = 21.688(2) Å, α = 91.90(2)°, β = 90.60(2)°, and γ = 102.45(3)°. The structure was plotted in the ORTEP (Ishizawa et al., 2013) and DIAMOND (Kamoun et al., 1991) software.

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Fig. 1

Photograph of a single crystal (a) and ORTEP representation of the geometric configuration of the constituent of C₂₉H₂₆N₃(NO₃)₃ (b).

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2.2 Synthesis of 1, 1, 4, 7, 7-pentamethyldiethylenetriammonium trinitrate

The PMDT compound was synthesized by mixing a solution of 3 mmol of HNO₃ in 10 ml of water and a solution of 1 mmol of 1,1,4,7,7-pentamethylethylenetriamine in 10 ml of water. The mixture was stirred for 15 min and then kept at room temperature. After several days, a colorless PMDT single crystal was obtained.

2.3 Computational methods

In this study, the PMDT structure was optimized at the DFT/B3LYP/6–31++G(d, p) level of theory using the Gaussian package (Frisch et al., 2009) with the Chemcraft visualization software (Zhurko and Zhurko, 2005). The non covalent interactions were investigated using the topological analysis in the AIMALL package (AIMAll (Version 19.10.12), 2019). To further confirm the bonding property, the ELF and LOL methods based on the Multiwfn 3.8 wave function analysis program were used (Lu and Chen, 2012,33). In addition, to deeper understand the non covalent interactions in the crystal, we carried out the Hirshfeld surface analysis in the Crystal Explorer program (Wolff et al., 2012). The RDG, IGM, and IRI approaches were implemented with the Visual Molecular Dynamics (VMD) program (Karaca et al., 2015) and the Multiwfn software. Then, NBO analysis in the Gaussian package at the same level of theory was performed. The MEPS has been computed at the B3LYP/6–31++G(d, p) level of theory to estimate electrophilic and nucleophilic sites. In addition, the ChELPG and Mulliken atomic charges were calculated by the DFT(B3LYP)/6–31++G(d, p) method. To investigate the reactive sites, the electrical behavior, and types of reactions in molecular systems, the FOMs were estimated by the TD-DFT method. To investigate the reactive sites, the electrical and types of reactions of molecular systems, FOMs was evaluated by using the TD-DFT method in gas, and some polar liquids (water and DMSO). The density of states (DOS) was plotted in the GaussSum program (Boyle and Vos, 2005). The thermal analysis and investigations of the electrical behavior of C₉H₂₆N₃(NO₃)₃ were also carried out. Finally, to predict the biological activity of the PMDT compound with the main antibacterial target proteins, the molecular docking was carried out using the iGEMDOCK software (Yang and Chen, 2004) and Discovery Studio Visualizer (Visualizer, 2005).

3.1 X-ray diffractometry

X-ray diffraction analysis was the main technique used by us to obtain crystallographic data and perform crystal refinement of the compound. The results are given in Table S1. In Fig. 1.b, one can see an ORTEP representation of the C₉H₂₆N₃(NO₃)₃ structure, which contains three independent nitrate groups NO₃^– and a 1,1,4,7,7-pentamethyldiethylenetriammonium (C₉H₂₆N₃³⁺) organic cation. The projection of this structure on to the PMDT $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ axes is shown in Figure S1. It can be seen in Figure S1.a that the organic cation and nitrate anions are linked by N—H…O and C—H…O hydrogen bonds, there by forming layers parallel to the ( $\overrightarrow{\mathrm{a}}$ , $\overrightarrow{\mathrm{b}}$ ) plane located at z = ¼ and z = ¾. The projection of the investigated crystal structure on to the $\overrightarrow{\mathrm{b}}$ axis (FigureS1.b) shows that the inorganic anion developed in the ( $\overrightarrow{\mathrm{b}}$ , $\overrightarrow{\mathrm{c}}$ ) plane are grafted to the organic cation centered at × = ½. These two units (NO₃^– and C₉H₂₆N₃³⁺) are linked by N—H…O and C—H…O hydrogen bonds. The hydrogen bond interactions in 1,1,4,7,7-pentamethyldiethylenetriammonium trinitrate are summarized in Table 1. The hydrogen bond motif in the PMDT molecule is presented in Figure S2. The cohesion in the PMDT structure is ensured by two weak C—H…O and N—H…O hydrogen bonds. Three hydrogen bonds connect the organic group to oxygen atoms of the nitrate unit with donor acceptor distances ranging between 2.750(3) and 3.132(2) Å. We note that each hydrogen (H1, H2, and H3) has two acceptor atoms and one donor atom generating the R₁²(4) motif. Thus, the crystal structure under study is established to nitrate anions by three centers or bifurcated hydrogen bonds. The donor–acceptor distance averaged over nine C—H…O hydrogen bonds is 3.31 Å.Furthermore, according to the Brown's criterion (Brown and Wu, 1976), hydrogen bonds are considered weak at d (D…A) > 2.73 Å (at d (D…A) > 2.73 Å, a hydrogen bond is considered strong).

3.2 Vibrational study

The title compound was characterized in the solid state by using the FTIR spectrum. The experimental IR spectrum was measured between 500 and 4000 cm⁻¹. Of the 12 theoretically planned modes, only 6 modes are active in IR. The IR absorption spectrum (Figure S3) of PMDT molecule shows 10 vibration bands in the frequency domain 1500–660 cm-1. We note for the vibrations of valence and deformation the presence of a band in addition to the expected number. An additional symmetric band observed in the vibration domain (υ_sNO₃^-) is due to the stretching vibrations δ(C—N). The additional anti-symmetric band observed in the domain (υ_asNO₃^-) corresponds to the deformation vibrations δ(CH3) in the symmetrical plane. The additional band noticed in the domain (δNO₃^-)can be attributed to the elongation vibrations ʋ(C—C) (Carbon skeleton, linear chain) and that in the domain (δNO₃^-)is due to the deformation vibrations in the δ(CH2) plane (swaying or roking). Also, the broadening of the spectrum (FigureS3.a) and the intense IR band (Figure S3.b) between 2696 and 2500 are assigned to C—H…O stretching mode.

3.3 Molecular geometry

The method and basis used in this study were selected using the calculated total energy. Therefore, the most stable structure with the minimum absolute value of the energy (E = -1363.84 a.u.) of 1,1,4,7,7-pentamethyldiethylenetriammonium trinitrate was obtained using the Gaussian software. To determine the ultimate structural parameters (bond length and bond angle) of the compound, we used the DFT(B3LYP)/6–31++G (d, p) hybrid method. The results obtained are given in Table S2 in comparison with the experimental data and presented graphically with numbering of atoms in Figure S4. It can be seen from the table that the theoretical values are very similar to the X-ray diffraction data. There are twenty-one C—H, nine N—C, nine N—O, four O—H, and three N—H bond lengths and one C—C bond length in the investigated molecule. The C—H bond lengths in the 1,1,4,7,7-pentamethylethylenetriammonium cation range within 0.959–1.515 Å. The N-C bonds lie between 1.491 and 1.504 Å (theory) and 1.476(5) −1.499 Å(experiment). The DFT-computed length of nine N-O bonds was found to be 1.223–1.319 Å, which agrees well with the XRD data (1.203–1.250 Å) for this bond. The observed O—H bond distances were 1.513 Å for H₃₇-O₄₅, 4.229 Å for H₂₉-O₄₂, 2.687 Å for H₂₂-O₅₀, and 4.268 Å for H₂₁-O₅₀. The DFT and XRD N₁-H₃₆, N₂-H₃₇, and N₃-H₃₈ bond lengths were found to be 1.132, 1.099, 1.122 Å and 0.90(3), 0.87(3), 0.87(3) Å, respectively. The maximum bond angle was observed for O₄₀-N₃₉-O₄₂ (123.4, 117.7(3)°) and the minimum bond angle, for C₂₀-H₂₁-O₅₀ (23.6°). Each organic entity is bound to nitrate anions through N—H…O and C—H…O hydrogen bonds. The calculated C—H…O and N—H—O bond angles range between [107.9–171.6]° and [114.8–31.7]°, respectively. These results show that the hydrogen bonding in the compound under study is weak. In Table S2, one can see the difference between several experimental and calculated parameters, which can be attributed to the fact that the theoretical computation was performed for the isolated molecule in the gas phase, which causes the deviation of the theoretical values from the XRD data obtained on the single crystal. In addition, we calculated the root-mean-square deviation (RMSD) to compare the theoretical geometric parameters with the experimental ones. A small RMSD value is generally preferred as it is indicative of a good fit to the data. Our results show that the computed parameters are in good agreement with the experiment.

3.4 Atoms-in-Molecule theory

At this stage of our study, we use the Bader’s AIM quantum theory to investigate the NCI in the PMDT compound. This approach based on the analysis of the topological properties of the charge density and its quality depends on a chosen computational level. To understand the interaction of hydrogen bonds, the topological parameters at bond critical points (BCPs) were determined in the AIMall calculation package. The electron density ρ(r) and its Laplacian ∇²ρ(r) play a vital role in verifying the strength and nature of chemical bonding (Harzallah et al., 2022). In addition, the kinetic energy density G(r), the total energy density H(r) [H(r) = G(r) + V(r)], the potential electron density V(r), the ellipticity ε, and the interaction energy E_interaction (E_interaction = V/2 (Noureddine et al., 2020) were used to elucidate the nature of hydrogen bonds (see Table 2). The parameter V_BCP describes the ability of a system to concentrate electrons at the BCPs, the G_BCP represents the tendency of electrons to spread out in space, and the parameter H_BCP stands for the electron density and bonding types (Noureddine et al., 2020). Firstly, of all, to check the validity of the data on the bond characteristics, we considered the BCPs obtained at the hydrogen bonds in the PMDT molecule. The PMDT molecular graph consists of various spheres colored differently in Figure S5.Green and red spheres correspond to the BCPs and ring critical points (RCPs), respectively. It can see from Figure S5 and Table 2 that the compound under study contains hydrogen bonds of two types: C—H…O and N—H…O. The results obtained suggest that the C—H…O and N—H…O interactions are low-energy. The weakness of these bonds is confirmed by the positive Laplacian ∇²ρ(r) and the total energy density H(r) values. On the other hand, the positive ∇²ρ(r) values include the weak vdW interaction and hydrogen bond interactions. In addition, to describe rigorously the nature and strength of the hydrogen bond interactions in the PMDT molecule, we calculated the binding energy (BE).It was determined for the electron density ρ_BCP at the BCPs of hydrogen bonds using the following equation with a mean absolute percentage error (MAPE) of 14.7% (Emamian et al., 2019):

The hydrogen bond interaction types can be classified and characterized according to different aspects (Emamian et al., 2019). The BE values calculated for the interactions of different types are given in Table 2. In this study, all the bonds formed between N—H…O and C—H…O are classified as weak-medium. In the studied compound, the BE is higher than 2.5 kcal/mol but it is lower than 14 kcal/mol, that is why we can said that the H-bonds, in this compound, is an electrostatic interactions type (Medimagh et al., 2021; Agwupuye et al., 2021). Therefore, the AIM analysis clearly showed how the cation and anion layers are interconnect through weak N—H…O and C—H…O hydrogen bonds.

3.5 Electron localized function and Local orbital Locator analysis

To explore the NCI, we carried out the ELF and LOL topological analyses. These tools are widely used to establish the atomic shell structure and classify chemical bonding on molecular surfaces (Noureddine et al., 2020). The ELF and LOL pictures were created using the Multiwfn wave analyzer package. These methods are based mainly on the localization of electrons in the Lewis structure. The ELF and LOL images for the investigated molecule are presented in the form of color shade maps and contour maps in Fig. 2. The blue-to-red color scale reflects the values from 0 to 1 for the ELF image, while the LOL scale ranges from 0 to 0.8. The red color around hydrogen atoms H11, H5, H17, and H38 in Fig. 2.a with the high ELF value shows the presence of bonding and nonbonding electrons. The blue color around few carbon and nitrogen atoms shows the area where the electron is expected to be delocalized. It can be seen in Fig. 2.b that the central region of a hydrogen atom is white; i.e., the electron density exceeds the color scale upper limit (0.8). The red area near hydrogen atoms H11, H17, and H5 indicates that the maximum LOL value is related to the covalent bonds between the atoms. In addition, the large blue values between the atoms of organic and inorganic groups highlight the presence of weak C—H…O and N—H…O hydrogen bonds. Thus, the ELF and LOL data are consistent with the results of the XRD and AIM study.

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Fig. 2

Plotting maps of: (a) ELF and (b) LOL of the PMDT.

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3.6 Hirshfeld surface analysis

The Hirshfeld surface analysis is a graphical method, which was used by us to study and visualize inter- and intramolecular interactions within the crystal packing of the PMDT compound. In this study, we attempted to obtain more information about the NCI in the crystal structure using the Crystal Explorer program. Figure S6 illustrates the asymmetric unit (Figure S6.a), mapped molecular Hirshfeld area at d_norm from −0.560 to 1.192 (Figure S6.b), and full 2D plot of C₉H₂₆N₃(NO₃)₃ (Figure S6.c). Different data on hydrogen bonds discussed in the X-ray Diffractometry Section are efficiently summarized in the d_norm mapping. Several dark-red circular spots in this map are related to the dominant contribution of the O…H/H…O contacts in the Hirshfeld surface plots; these spots correspond to the N-H…O and C—H…O hydrogen bonds. Other (blue and white) spots in this map are related to the H…H contacts. The d_norm mapping shown in Figure S7 gives a general overview of some hydrogen bonds involved in the maintenance and stability of the investigated crystal structure. In addition, we calculated the electrostatic potentials using the Tonto and mapped it on the Hirsheld surface using the STO-3G base fixed at the Hartree-Fock theory level over a range of ± 0.27 a.u. (Figure S8). Indeed, the donor atoms of hydrogen bonds are presented by the positive electrostatic potential (blue regions), while the acceptor atoms are presented by the negative electrostatic potential (red regions). Figure S9 illustrates the 2D fingerprint plot distribution for the C₉H₂₆N₃(NO₃)₃ compound. The distribution shows that the O…H/H…O intermolecular contacts occupy 70.4% of the entire Hirschfeld surface and appear as two symmetrical wings with a large, long point of the sum d_e + d_i ∼ 1.8 Å smaller than the sum of the vdW radii of hydrogen (1.09 Å) and oxygen (1.52 Å) atoms. The H…H contacts occupy almost ¼ (23.7%) of the entire Hirschfeld surface; they can be seen in the fingerprint plot as a distinct tip with d_i = d_e = 1.2 Å, which is greater than the vdW radius of the hydrogen atom (1.09 Å). Indeed, the organic part has a large number of hydrogen atoms (SH = 60.4%) on its molecular surface, while carbon atoms are rarely met on it (SC = 0%), because they conventionally form four bonds with other atoms. The rest N…H/H…N, O…O, and N…O/O…N contacts occupy 3%, 1.9%, and 1% of the Hirschfeld surface, respectively. The intermolecular interactions in the investigated crystal were evaluated using the ratio of enrichment (RE), a new descriptor based on the Hirschfeld surface analysis. The REs of intermolecular contacts involved in the C₉H₂₆N₃(NO₃)₃asymmetric unit are given in Table S3.

3.7 Reduced density gradient analysis

To obtain more information about the bond interactions, we applied the RDG analysis, a well-known computational tool for exploring non covalent interactions in molecular systems (Medimagh et al., 2021). The RDG is a color scaling of interactions: the surfaces are colored in blue (hydrogen bonding), green (vdW interaction), and red (steric effect).These interactions are based on the electron density property. The RDG and sign (λ2)ρ plots for the molecule under consideration were built using the Multiwfn and VMD software. In our case, different interactions were disclosed in the PMDT monomer form (Fig. 3). The analysis of the plots revealed three sites of interactions. The light-blue isosurfaces are identified between the organic and inorganic units and characteristic of weak (C—H…O and N—H…O) interactions. The blue contour in the RDG scatter plot around −0.020 a.u. indicates the strong attraction between the C—H…O and N—H…O hydrogen bonding interactions. In addition, one can see the mixed red-green color near the nitrate anion and 1,1,4,7,7-pentamethylethylenetriammonium cation. In the RDG scatter spectra, the mixed red-green spikes between 0 and 0.015 are indicative of the hydrogen bonding and C—H…π interaction. The results of the RDG analysis confirm the hydrogen bonding interactions in the PMDT molecular structure.

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Fig. 3

RDG images of C₉H₂₆N₃ (NO₃)₃.

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3.8 Independent gradient model

At this stage, we used the IGM to analyze the weak intra- and intermolecular interactions. The IGM analysis is a clearly comprehensible and physically meaningful approach for visualizing the hydrogen bonding and vdW interactions (Medimagh et al., 2021). Fig. 4.a presents the 2D colored map of the sign(λ₂)ρ function on the δg isosurface plotted in the Multiwfn and VMD packages. The δg versus sign(λ₂)ρ scatter plot was used to reveal and distinguish the attractive, repulsive, and vdW interactions. The blue, red, and green areas in the scatter maps correspond to the strong interaction, weak interaction, and repulsion, respectively. There are three peaks (peak 1, peak 2, and peak 3) in the sign (λ₂)ρ rangefrom-0.05 to 0.05. Peak 1 is a fuzzy greenish-blue peak located at sign(λ₂)ρ ≈-0.02 and pointing out the presence of a weak hydrogen bond. Around the sign(λ₂)ρ values of-0.01 and 0.015, green peaks 2 and 3 are observed. Since these sign(λ₂)ρ values are close to zero, the peaks are indicative of the vdW interaction. Thoroughly analyze the intra- and intermolecular interactions, we explored strong and weak interactions in the investigated molecule by the IGM method using a wave function scheme presented in Fig. 4.b. This scheme allowed us to detect and calculate the total electron density gradient attenuation caused by the inter atomic interaction. As can be seen in Fig. 4.b, all the chemically bound regions have the larger δg (above 0.2) values (white areas). The red area around hydrogen and nitrogen atoms reflects the high electron density.

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Fig. 4

(a) isosuface scatter plot of δg vs sign (λ2)ρ and (b) plotting plane map of PMDT.

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3.9 Interaction region indicator analysis

In this study, we used the IRI method to map and analyze weak-interaction regions in the investigated molecule. The IRI is a new real-space function, which can identify all kinds of interactions in chemical systems simultaneously (Sagaama et al., 2021).The IRI differs from the RDG by a constant factor (an adjustable parameter), which plays a vital role in balancing between the covalent and NCI. The IRI equation is

This is a very simple function, which only depends on the electron density and its gradient. Similar to the RDG and IGM methods, the sign(λ2)ρ function on an IRI isosurface is plotted to distinguish the attractive (hydrogen bond), repulsion (steric effect), and vdW interactions. In Fig. 5, the IRI isosurface map and the scatter map between the IRI and sign (λ2)ρ function of the PMDT compound are presented. In Fig. 5.a, we can see several green spots between the organic and inorganic compounds, which correspond to the vdW interaction. In addition, the light-blue color reflect the presence of hydrogen bond interaction between the C–H group of the (C₉H₂₆N₃)³⁺ cation and the oxygen atom of the (NO₃–) anion. IRI isosurfaces indicate that the carbon–carbon covalent bond were established and characterized by blue color. The scatter map between the IRI and sign (λ2)ρ in Fig. 5.b makes it possible to establish the IRI distribution character. Four spikes in the scatter map correspond to the IRI minimum. The spikes at sign (λ2)ρ = -0.258, 0.250, and −0.100 a.u. correspond to │ $\mathrm{\nabla }\mathrm{\rho }$ │=0 and │ $\mathrm{\nabla }\mathrm{I}\mathrm{R}\mathrm{I}$ │=0. This verifies the correlation between the IRI map and AIM analysis data (Lu and Chen, 2021). On the other hand, the spike around sign (λ2)ρ = 0 corresponds to│ $\mathrm{\nabla }\mathrm{\rho }$ │≠ 0 and │∇IRI│=0, i.e., to weak intermolecular interactions.

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Fig. 5

Same maps of PMDT: (a) isosurface map of IRI,(b) scatter map between IRI and sign(λ2)ρ.

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3.10 Natural bond orbital analysis

The NBO analysis known as an efficient tool for studying intra and intermolecular interactions between bonds. It provides a convenient basis for exploring charge transfer within a molecule (Kazachenko et al., 2021). This later was used to disclose possible bonding interactions between donor and acceptor atoms in the PMDT compound. We carried out the NBO analysis of the investigated compound at the DFT(B3LYP)/6–31++G(d, p) level of theory. The data on the second-order energy E(2) for weak interactions in the PMDT molecule are given in Table S4. Hydrogen bonds are believed to be caused by charge transfer from the lone-pair (LP) orbital’s to antibonding σ*(X-H) ones. In addition, the interaction energy significantly affects the strength of a hydrogen bond. The most significant energy interactions between the donor and acceptor NBOs were found forLP₂ (O₄₁) → σ*(N₃-H₃₈), LP₂ (O₄₅) → σ*(N₂-H₃₇), and LP₂ (O₄₉) → σ*(N₁-H₃₆), which results in the enormous stabilization of energies of 81.76, 66.58, and 89.58 kcal/mol, respectively. This means that the N–H…O interaction makes a considerable impact on the crystal packing in the investigated compound. Similarly, the weak NBO interactions LP₃ (O₄₄) → σ*(C₁₃-H₁₅) and LP₂ (O₄₄) → σ*(C₁₃-H₁₅) suggest the existence of C–H…O hydrogen bonds, which have a higher stabilization of energies of 3.02 and 1.63 kcal/mol, respectively. In addition, it was demonstrated that N–H…O and C–H…O hydrogen bonds contribute to the stabilization of the 1,1,4,7,7-pentamethyldiethylenetriammonium trinitrate compound.

3.11 Molecular electrostatic potential surface analysis

In this section, we have effected a molecular electrostatic potential analysis to predict the chemical reactivity of our molecule. This method is related to the electron density and is a very useful descriptor for understanding the electrophilic and nucleophlic sites as well as hydrogen bonding interactions (Issa et al., 2020). The MEPS was mapped to a different range of colors varied from red (negative potential region) to blue (positive potential regions) as shown in Figure S10. The MEPS plot is generated using the same level of theory DFT with B3LYP/6–31++G(d, p) basis set in the gas phase and with various solvation (water and DMSO). The color code of the compound lies in the range of 6.734e-2 to −6.734e-2 a.u. The examination of all MEPS: in gas, in water and in DMSO solvent, shows that the most negative potential region (red color) are localized over around the oxygen atoms of the trinitrate units (inorganic group).It can be seen that the most negative potential region (red) is localized around oxygen atoms of the trinitrate units (the inorganic group). This region should contain the sites favorable for the possible electrophilic reactivity and point to the electron rich region. Similarly, the most positive sites (blue) are localized mainly around C₉H₂₆N₃⁺(i.e., around hydrogen atoms), which point to electron deficient sites and the sites more reactive for the nucleophilic attack. According to the electrostatic potential surface analysis results reported in (Harzallah et al., 2022), the hydrogen bond identified as a donor–acceptor interaction. It proves the fact that the electrostatic potential of the donor becomes less negative as the acceptor becomes more negative. It can see in Figure S10 that hydrogen atoms act as acceptors and oxygen and nitrogen atoms, as donors. Thus, the MEPS analysis confirmed the existence of C—H…O and N—H…O hydrogen bonds in the structure of the investigated molecule.

3.12 ChELPG electrostatic population and Mulliken atomic charges

Atomic charges of molecular systems calculated by several available methods, including the Mulliken population analysis and the ChELPG scheme. These methods were used to describe the electron charge distribution in a molecule. The analysis of a partial atomic charge helps one to identify donor and acceptor sites of molecular systems (Sagaama and Issaoui, 2020). The Mulliken population analysis describes the electron charge distribution in a molecule, while the ChELPG method is based on fitting of the molecular electrostatic potential (MEP) (Sarala et al., 2021). The results of the computations in the Multiwfn package (Patel et al., 2004) are given in Table S5. It is noteworthy that the Mulliken atomic charge and ChELPG data are very similar, except for some cases, which evidences for the efficiency of the method used. Both methods showed that all hydrogen atoms in the PMDT molecule are positively charged. This was obvious from the discussion of the MEPS data (see Section 3.10), which pointed out the electron deficient sites (the blue region) on hydrogen atoms. The charges in the ChELPG scheme are negative for all carbon atoms, except for C7 (-0.375 a.u.) and C10 (-0.232 a.u.), which interact with the positively charged atoms (H8, H10). Meanwhile, the Mulliken population analysis showed that the charges of carbon atoms have negative values. Furthermore, the charges of all oxygen atoms are negative, except for O44 (0.066 a.u.) and O45 (0.050 a.u.), which are charged positively in the Mulliken charge analysis and negatively according to the ChELPG scheme. The highest negative charge on oxygen, nitrogen, and carbon atoms is indicative of the formation of intermolecular interactions with hydrogen atoms (the formation of hydrogen bonds).

3.13 HOMO-LUMO calculation

The frontier molecular orbital (FMOs) analysis play a vital role in exploring the kinetic stability, conductivity, electrical proprieties and chemical reactivity of molecular structure (Medimagh et al., 2021). The band gap defined as the difference between HOMO and LUMO that explains the stability of the molecule. The HOMO is noted as a nucleophile that donates electrons, whereas LUMO act as an electrophile that accepts electrons. In this light, we performed a calculated quantum chemical descriptors of PMDT compound at DFT/B3LYP/6–31++G(d, p) level of theory in gas, water and DMSO solvation (Table S6). The distribution and the energy gap of these orbital's was illustrated in Figure S11. It is clear from this figure; the red color indicates the positive phase, while the green color indicates the negative phase. As shown also that the HOMO and LUMO are entirely localized on the nitrates groups with a small contribution of a few carbon and nitrogen atoms of organic unit. The gap energy is critical parameters to determine the stability and the chemical reactivity of the studied molecule. A hard molecule is characterized by a large HOMO-LUMO gap while a soft with a small gap (Kazachenko et al., 2021). In addition, the ΔE_HOMO-LUMO measures the excitability of the molecule, the weaker the energy, more easily it can be excited and inversely. Not only, has a large/small gap indicated high/low stability and low/high chemical reactivity (Medimagh et al., 2021), respectively. As shown in Table S6, other parameters such as chemical potential (μ), global electrophilicity index (W), global hardness (η) and softness (S) can also describe the stability and reactivity of a compound. In the present case, the energy gap (ΔE) value is equal to 5.40 eV (in gas), 5.79 eV (in DMSO) and 5.82 eV (in water). We noted that there is not a big difference between the energy gap values in water, DMSO and in gas. This will demonstrate the intra molecular charge transfer and molecule stability also during solvation. Furthermore, the electrophilicity (w) is greater than two in gas and various liquids. This explains that our molecule is strong electrophile and contributes easily in polar process. The maximal amount of electronic charge Q^max is calculated in water (1.56 eV), DMSO (1.59 eV) and gas (1.60 eV). This parameter is used to describe the propensity of the system to acquire additional electronic charge from the environment. We remark from Table S6, that Q^max (gas) > Q^max (DMSO) > Q^max (water). This result indicates that PMDT compound in gas phase is more prone to receive extra electronic charge that under the effect of solvation.

• Density of States Spectrum Analysis

The DOS spectrum was obtained in the GaussSum program to calculate contributions of the groups to the HOMO and LUMO. The DOS spectrum analysis provides information important for predicting the nature of interactions between different groups (Fradi et al., 2021; Medimagh et al., 2021). The positive DOS value is related to the bonding interactions, while the negative and zero values correspond to the antibonding and nonbonding ones, respectively. The pictorial illustration of DOS for the PMDT compound in various solvation (water and DMSO) and in the gas phase, shown in Figure S12. From the DOS picture, the green and red color lines explain HOMO (E_H) and LUMO (E_L) levels, respectively. In addition, the DOS indicates the energy gap ΔE of the title compound PMDT at the same level of theory. We noted form this figure that the values of the HOMO, LUMO and the energy gap │ΔE_HOMO-LUMO│are comparable with the values obtained by the DFT calculation. In DOS picture, we note that the values of the energy gap are close in gas and under the effect of solvation. Further, the values of the energy gap are large (>3 eV) implies a high kinetic and thermodynamic stability of our compound PMDT (Zhang et al., 2010).

3.14 Temperature behavior of the C₉H₂₆N₃(NO₃)₃Compound

3.14.1

3.14.1 Differential thermal and thermogravimetric analysis of the C₉H₂₆N₃(NO₃)₃ compound

The DTA/TGA curves for 1,1,4,7,7-pentamethylethylentriammonium trinitrate were built for the sample with a weight of m = 29.13 mg in the argon atmosphere upon heating from room temperature to 773 K at a rate of 10 K ∙ min-¹ (Figure S13). The DTA curve shows that the material under study decomposes in the two similar stages:

(i)The first exothermic peak appears in the TGA curve around 415 K and corresponds to a significant weight loss. This peak reflects the first decomposition stage. At this stage, proton transfer between the cationic and anionic parts occurs at high temperatures, which causes an internal redox reaction between the amine and nitric acid (Scheme 1). The proton transfer to NO₃- anions is related to the weakness of N–H bonds in the condensed phase at high temperatures (Gatfaoui et al., 2019).

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Scheme 1

Decomposition of PMDT. TP: Proton transfer, MMR: Redox reaction.

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(ii) The second exothermic peak centered at 544 K corresponds to the rest part of the decomposition process:

3.15 Study of the ionic conductivity of the C₉H₂₆N₃(NO₃)₃ compound

The imaginary part Z’’ of the complex impedance as a function of its real part Z’ was explored at temperatures from 298 to 373 K. In Fig. 6.a, the experimental points form arcs of a circle passing in the proximity of the origin of coordinates and centered below the real axis. The values of resistance R at different temperatures are determined by the intersection of the Nyquist diagram and the × axis. An increase in temperature is accompanied by a gradual decrease in the resistance. Figure S15 shows the conductivity evolution upon temperature variation. The conductivity values for the compound obtained at different temperatures are given in Table S7. Figure S15 shows the Ln(σT) = f(10³/T) plot, which is a straight without breaks consistent with the Arrhenius law with an activation energy of E_a = 0.26 eV. The conductivity data were confirmed by the thermal investigations, which revealed no thermal accidents in this temperature range. Fig. 6.b and 6.c illustrate the changes in the Z’ and Z’’ values upon frequency variation at different temperatures. It can be seen in Fig. 6.b that, at low frequencies, the Z’ values are almost invariable. Starting with a certain frequency, Z’ slowly decreases and tends asymptotically to zero at high frequencies. Similarly, Z’ decreases with increasing temperature. Fig. 6.c shows that, in the spectrum Z’’= f (logf), the peaks (ω_max, Z’’_max) appear, the intensity of which decreases with increasing temperature. These peaks reflect the electrical relaxation phenomenon. They shift toward higher frequencies as the temperature increases; i.e., the relaxation phenomenon depends on temperature (Ouerghi, 2018; Wacharine et al., 2007). Figures S16.a and S16.b show the real and imaginary parts ε’ and ε’’ of the permittivity as functions of temperature and frequency. It is noteworthy that the ε’and ε’’values decrease with frequency at different temperatures. This results show that strong permittivity dispersion are observed with increasing temperature. In addition, as the frequency increases, these two dielectric characteristics decrease, this can be explained by the fact that dipoles existing in the system cannot quickly reorient to follow the frequency of the electric field at which the polarization orientation stops (Wang et al., 2021; Gatfaoui et al., 2017). On the other hand, the high ε’and ε’’values at low frequencies point out the existence of the electron polarization (Elwej et al., 2015; Hajlaoui et al., 2015).

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Fig. 6

(a) Evolution of the impedance spectra as a function of the temperature, (b) Variation of the real part Z’ and (b) the imaginary part Z’’ depending on the frequency at different temperatures.

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