Explosives properties of high energetic trinitrophenyl nitramide molecules: A DFT and AIM analysis

3.1 Structural aspects and heat of formation

The TNPA molecules were optimized at a higher DFT level method [B3LYP] using both polarized and augmented basis sets of 6-311G^∗∗ and cc/pVDz respectively (Fig. 2) to analyze their topological properties which decide the sensitivity toward external shock. The C—N bonds in the aromatic rings were found to be exhibiting an average bond lengths of ∼1.48 Å without notable variations in polarized and augmented basis operations. The bond lengths of the C—C bonds in the aromatic ring for each molecule were found to be ∼1.39 Å, with the shortest bond appeared between C(2)—C(3) atoms of the ring; notably, the C—C bond lengths are found to be well in agreement with the standard C—C bonds (Lide, 1967). A feasible impact was notified for the N(16)—N(17) and C(6)—N(16) bonds with corresponding variation of ∼0.1 Å and ∼0.2 Å for the augmented and polarized basis set operation. Further analysis on N—O bonds showed that the interaction was consistently exhibiting a bond lengths of ∼1.2 Å in all TNPN molecules without much variations, indicates the stability of the bond, with N(17)—O(19) being the shortest and N(22)—O(24) being the longest bond with 1.20 Å and 1.23 Å respectively for NETNPN. The results of the structural studies thus justified the invariance of the bond lengths associated with the molecules with different basis set operations.

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Figure 2 Optimized structures of MTNPN, ETNPN and NETNPN molecules at B3LYP/aug-cc-pVDZ.

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As the bond length analysis exposed the unvarying nature of the bondlengths, researchers aimed to study the deviation and the distortion caused to the molecules due the presence of the nitro functional groups. The molecules, MTNPN, ETNPN and NETNPN were subjected for geometrical analysis and the results were tabulated (Table 2) and interpreted as well. The studies showed that the bond angle of C—C—C atoms of the aromatic ring was found to be standard (Sutton, 1965), exhibiting ∼120°, with an observed exception for the C(1)—C(6)—C(5) bond angle of ETNPN and NETNPN. The concerned bond angle exhibited a lower value of 116.1° and 117.2° respectively for each structure. The orientation of nitrogen atoms attached to the aromatic ring also revealed the bond angle ranging from 115° to 121°, with C(4)—C(5)—N(10) making a least angle of 115° for MTNPN. Further studies over the nitro groups in the non-ring region of the molecules showed N(17) atoms are deviated from the corresponding terminal carbon atoms (C(20), C(21) and C(20) for MTNPN, ETNPN and NETNPN respectively) with a variation from 117° to 119°, a maximum deviation of 119.19° observed for N(17)—N(16)—C(20) of NETNPN, which might be due to the extra NO₂ group attached to the C(21) atom. The distortions of the bonds were thoroughly studied by resolving the torsion angles of each system of molecule in detail. The studies to investigate the torsional distortions of the molecules exposed that the nitro group attached to the C(3) atoms of each structures is in planar with the aromatic ring. It can also be found that the transposition of O(14) with respect to C(2) justifies the stability of the linkage by making a dihedral angle ∼180° for each structures. Further analysis on the remaining nitro functional groups exposed the gauche position of O(11) with C(4) for the torsion angle is ∼32° with concerned aromatic carbon. A slight cis conformation can be observed in NETNPN for the nitro group attached to C(1), with torsion angle of 28° [C(2)—C(1)—N(7)—O(9)]. The review of the torsion angle of the chemical bond which links the aromatic ring and phenyl substituent of the molecule via C(6)—N(16), showed that the bond is twisted to make an anticlinal conformation with the ring, thereby exhibiting the non-planar geometry of the molecule. The concerned torsion angle, C(1)—C(6)—N(16)—N(17) was found to be ranging from ∼121° to ∼91° corresponding to each structures, in which NETNPN makes the least bond twist of 91.9°. An individual result was observed for the cis conformation of C(6)—N(16)—C(20)—C(21) of NETNPN in which a dihedral angle difference of ∼6° was observed due to the basis set effect. Apart from this observation, the investigation revealed the insignificant effect of the basis set operation over the geometrical structure of the molecules.

3.2 Electron density

AIM theory (Bader, 1990) is a pioneer tool to analyze the charge density distribution and the electrostatic properties for the gas phase molecules from quantum chemical theory. A bcp search on all bonds of the molecule has been carried out to characterize the electron density at the BCP, in which a (3, −1) type of critical point was found for all bonds of TNPN molecules from the polarized and augmented basis sets. The bond topological parameters of electron density at the critical points of each bond have been determined and are listed in Table 3. Fig. 3 shows the deformation density map of three TNPN molecules. The electron density ρ_bcp(r) of aromatic C—C bonds of the three molecules are almost equal and the average value is ∼2.11/∼2.08 eÅ⁻³ in 6-311G^∗∗/aug-cc-pVDZ basis sets and this value agrees with the reported structure having similar C—C bonds (Stephen et al., 2011). Because of the phenyl substituent at C(6) atom, the ρ_bcp(r) of C(1)—C(6) and C(5)—C(6) bonds reduced feebly [0.07 eÅ⁻³] when compared to the rest of C_aro—C_aro bonds. Also, the maximum deformation density has been noticed for C≡C bond [∼2.60 eÅ⁻³] in NETNPN molecule among the non-ring C—C bonds of all the three analogue molecules, which reveals its triple bond nature. From the spectrum of the deformation density of all the bonds in the TNPN molecules, the charge accumulation in C—NO₂ bonds is found significantly low with an average value ∼1.74 eÅ⁻³ which agrees well with the reported structures (Stephen et al., 2010). From Fig. 3, the deformation density of —NO₂ groups reveals the orientation of oxygen loan pair electrons. As expected, the maximum electron density distribution is predicted for N⚌O bonds of nitro groups and the values are ∼3.42 and ∼3.39 eÅ⁻³ from both the levels of calculations. Notably, the non-ring C—N bonds carry different densities, and among these the maximum electron density is predicted for C(20)—N(16) [∼2.27 eÅ⁻³] in NETNPN molecule when compared to the C(6)—N(16) [∼1.95 eÅ⁻³] and C(21)—N(22) [∼2.10 eÅ⁻³]. The lowest bond density was found for C_aro—NO₂ bonds [∼1.74 eÅ⁻³] in all the three TNPN molecules and non-ring C—N bonds [∼1.63 eÅ⁻³] in MTNPN and ETNPN molecules. The bond density for aromatic, ethyl and methyl C—H bonds is almost similar with an average value of [∼1.95 eÅ⁻³] from both the levels of calculations.

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Figure 3 Deformation density maps of TNPN molecules, Blue: positive contours; Red: negative contours and the zero contours are dashed lines. The contours are drawn at 0.05 eÅ⁻³ intervals.

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The position of bcp has been revealed from the bond path analysis of all three TNPN molecules, from which the bond charge polarization of each bonds has been calculated. Among the non-hydrogen atoms, C_aro—C_aro and N—N bonds are less polarized bonds which are confirmed from the small bcp shift of about ∼1.0/∼0.8 and ∼0.7/∼0.9 Å from both the levels of calculations. The maximum bcp shift [∼10.6/∼11.0 Å] from the bond midpoint has been noticed for the C—N bonds among the non-hydrogen atoms and bcp is pushed toward the respective carbon atoms. Both the levels of calculations result in the similar bcp shift for N⚌O bonds of about ∼2.4 Å from the bond midpoint. In the whole spectrum of bond charge polarization, the C—H bonds are highly polarized due to heavy and light atom interaction.

3.3 Laplacian of electron density

The Laplacian of electron density (∇²ρ_bcp(r)) at the bcp provides significant information about the charge concentration and depletion of chemical bonds, which allows predicting the strength of bonds and the type of interaction between the atoms in molecule (Bader et al., 1981). Here, the Laplacian of electron density and the energy density distribution of each bonds of the TNPN have been calculated for the three analogue molecules. Fig. 4 shows the Laplacian of electron density distribution of analogue molecules. The uniform charge density distribution in the contours of C_aro—C_aro bonds reveals their covalent bonding interactions and the ∇²ρ_bcp(r) values at bcp’s are almost equal: ∼−21/∼−18 eÅ⁻⁵. The effect of maximum electron density of C≡C bond in NETNPN molecule attributes that the bond charges are highly concentrated [−25.1/−20.8 eÅ⁻⁵]. Notably, its corresponding total bond energy density H(r) is also high and the average value is −3.51 HÅ⁻³. Both the levels of DFT calculations predict that the charges in C—NO₂ bonds are highly depleted and their ∇²ρ_bcp(r) values are ∼−16.1 and ∼−15.2 eÅ⁻⁵ respectively. This was further confirmed from the lowest bond energy density −1.83 HÅ⁻³. Next to C—NO₂ bonds, the bond charges are found to be highly depleted for N—N [N(16)—N(17)] bonds in MTNPN [−13/−15.9 eÅ⁻⁵], ETNPN [−13/−15.8 eÅ⁻⁵] and NETNPN [−5.9/−10.1 eÅ⁻⁵] molecules and C—N [C(20)—N(16)] bonds in MTNPN [−13.3/−13.5 eÅ⁻⁵] and ETNPN [−12.7/−12.2 eÅ⁻⁵] molecules, whereas in NETNPN molecule, the charges are concentrated [−19.3/−22.8 eÅ⁻⁵] in C(20)—N(16) bond. This unusual charge concentration may be due to the —CCNO₂ attachment with C(20) atom of NETNPN molecule. Invariably, the Laplacian values for all N⚌O bonds in NO₂ groups are found to be highly negative [∼−25.9/∼−25.6 eÅ⁻⁵], which reveals their concentration of bond charges at the bcp. It was further empathized from the high potential energy V(r) in the bonding region [∼−7.03/∼−6.95 HÅ⁻³]. Relatively, the negative Laplacian values for aromatic C—H bonds [∼−24.8/∼−27.7 eÅ⁻⁵] are feebly increased in comparison with that of methyl [∼−22.8/∼−24.3 eÅ⁻⁵] and ethyl C—H [∼−23.8/∼−25.2 eÅ⁻⁵] bonds, which show that the bond charges are considerably concentrated in C_aro—H bonds. The bond ellipticity [ɛ = λ₁/λ₂] analysis has been carried out for the study of spherical and aspherical nature of electron density at bcp. The bond charges are highly anisotropic for C_aro—C_aro [∼0.23] and charge depleted bonds C_aro—NO₂ [∼0.11] and N—N [N(16)—N(17); ∼0.28], whereas the ellipticity values for rest of the bonds show that the charges in the bonding regions are highly isotropic.

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Figure 4 Plots of negative Laplacian of electron density of TNPN molecules, The contours are drawn on a logarithmic scale, 3 × 2^N eÅ⁻⁵.

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3.4 Frontier molecular orbital energies

The molecular stability is usually measured in terms of the energies of the frontier orbitals (Fukui et al., 1952). It has been characterized from the energy gap between HOMO and LUMO. The higher the energy gap, compound is much more stable and the lower energy gap implies low stability of the molecule. The energies of frontier molecular orbitals and their gaps (ΔE_LUMO–HOMO) of MTNPN, ETNPN and NETNPN molecules were calculated at B3LYP/aug-cc-pVDZ level and are listed in Table 4. The comparative analysis of computed values of HOMO, LUMO and energy gap ΔE_LUMO–HOMO, indicates that MTNPN and ETNPN molecules were more stable than NETNPN as their ΔE_LUMO–HOMO values are −4.203, −4.267 and −3.881 respectively. The ΔE_LUMO–HOMO values of MTNPN, ETNPN and NETNPN were found to be different, and this modification is caused by the effect of different substituents attached in C(6) atom. The effects of —NO₂ groups on HOMO and LUMO are schematically shown in Fig. 5, which display the variation of ΔE_LUMO–HOMO. As it is known, LUMO is related to molecular electron affinity, Bader’s study showed that impact sensitivity of aromatic explosives will increase with decrease in LUMO energy, and so incorporation of —NO₂ group will increase sensitivity.

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Figure 5 Energies (in eV) of frontier orbital for TNPN molecules and showing the variations of ΔE_LUMO–HOMO.

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3.5 Oxygen balance and Impact sensitivity

Oxygen balance (OB) is one of the important properties of energetic material. It is defined as “the amount of oxygen, expressed in weight percent, liberated as a result of complete conversion of the explosive material to carbon dioxide, water, sulfur dioxide, aluminum oxide, etc.” (Akhavan, 2011; Li, 2010; Owens et al., 1985). Negative oxygen balance produces greater quantity of CO and positive oxygen balance produces more NO_x gases. The equation for the oxygen balance (OB) is,

Analysis of the impact sensitivity involves dropping a weight from the variable height over the explosive sample to make 50% probability of causing an explosion (50% impact height or h₅₀) exhibiting the relation that lesser the h₅₀ value higher the impact sensitivity of the molecule (Keshavarz and Jaafari, 2006). The impact sensitivity (h₅₀%) of the model compounds was calculated according to Eq. (4), from the electronic structures using charges obtained from electrostatic potential fitting methods (CHELPG) (Breneman and Wiberg, 1990) for the nitro (NO₂) groups. In nitro compounds, the C—NO₂, N—NO₂ and O—NO₂ bonds are usually the weakest bonds in the molecule, and these bonds are proven to break often at the initial steps of decomposition or detonation. The nitro group charge (Q_NO2) can be calculated by summing the net ESP charges of nitrogen (Q_N) and oxygen (Q_O1 and Q_O2) atoms.

The higher the negative charge of NO₂ group, weaker the electron-withdrawing ability and thus the greater the overall stability of the compound. As the number of NO₂ groups in the TNPN framework increases, competition for the available charge increases and thus the molecule becomes unstable. Further, using oxygen balance and the nitro group charges (QNO₂), we have calculated the impact sensitivity, h₅₀% of MTNPN, ETNPN and NETNPN molecules. This provides a new insight into understanding the effect of molecular structure in the impact sensitivity. Studies have been reported, which evaluate the impact sensitivity of the nitro molecules which agree well within the experimental bars, by correlating the nitro group charges with impact sensitivity (Murray et al., 1995; Politzer et al., 1991). A simplified relation with much accuracy has been reported in the investigations of Cao and Gao (2007) by quantifying the nitro group charges and oxygen balance, expressed in Eq. (4) with a standard error value of 0.54 m. Regression analysis of Eq. (4) by implementing square of the nitro group charges (QNO₂²) considerably reduced the standard error value to 0.19 m, which proved more accuracy with the experimental details, expressed in Eq. (5). The impact sensitivity of the molecules under concern (h₅₀%) was obtained from Eq. (5):

The predicted H_50% value for the MTNPN, ETNPN and NETNPN molecules is shown in Table 3, which reveals that h₅₀% values decrease as the number of NO₂ groups and other substituent group increases. This shows that the sensitivity increases from MTNPN to NETNPN. Thus inspecting the h₅₀%, Q_NO2 and OB₁₀₀ values, NETNPN molecule is more sensitive than MTNPN and ETNPN molecules.

3.6 Electrostatic potential and V_mid

The molecular electrostatic potential (MEP) explores the polarization, electron correlation, charge transfer effect and the reaction sites of the molecule (Murray et al., 2009). The molecular ESP allows identifying the electrophilic and nucleophilic sites of the molecule. Fig. 6, shows the electrostatic potential of the TNPN molecules for the isosurface values +0.5 and −0.5 eÅ⁻¹. A large electronegative region is found near NO₂ groups region, while the rest of the region is covered with positive surface. The high electronegative surface is the expected reaction surface of the molecule. This electrostatic information paves the way to predict the reaction surface of the molecule.

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Figure 6 Isosurface representation of electrostatic potential of TNPN molecules, Blue: positive potential (+0.5 eÅ⁻¹) and Red: negative potential (−0.5 eÅ⁻¹).

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The sensitivities of energetic compounds are related to the anomalous charge imbalance that is characteristic of their molecular surface electrostatic potentials. There are many ways the imbalance between positive and negative surface potentials can be quantified. The balance parameters (ν) can be calculated from the relation (Bulat et al., 2010).

The quantities ${\sigma }_{+}^2$ and ${\sigma }_{-}^2$ are the indicators of the strengths and variability of positive and negative surface potentials. The degree of balance between the positive and negative surface potentials is measured by ν. The balance parameter ν reaches a maximum value 0.25, when ${\sigma }_{+}^2$  =  ${\sigma }_{-}^2$ . Here, we have calculated the positive and negative electrostatic potential variances ( ${\sigma }_{+}^2$ and ${\sigma }_{-}^2$ ) and the electrostatic balance parameter (ν) of TNPN molecule from DFT method, and the corresponding values are shown in Table 5. The sensitivity of NETNPN molecule is further empathized from its highest ${\sigma }_{+}^2$ [176.60] values among the rest of the molecules.

The most notable feature of the electrostatic potential of energetic molecule is its important relation with the impact sensitivity. Here, we explore the concept proposed by Murray et al. (2009) regarding the buildup of positive ESP over C—NO₂ bonding region and to relate its impact sensitivity. To correlate the ESP with the impact sensitivity, we investigated the electrostatic potential V_mid at the bond mid points of the molecule, which is defined as